The lawsuit is the latest iteration of a now familiar spectacle in which federal courts are tasked with cramming a digital technology into the Procrustean bed of analog-era legal concepts. In this instance, the service looks quite dubious when viewed from 30,000 feet, but becomes more plausible as you get closer and start wading into the weeds.

Aereo, which launched on a limited basis in March, currently allows New York City residents to watch broadcast (but not cable) TV shows on their iPhones, iPads and web browsers, and to tape those shows and play them back later. The company has been sued for copyright infringement by all the major networks and local New York TV stations, including Disney’s (DIS) ABC, NBCUniversal (CMCSA), CBS (CBS), Fox (NWS), Telemundo and Univision. The plaintiffs claim that Aereo is engaged in the unauthorized, public retransmission of their over-the-air programming, and they seek a preliminary injunction to shut it down. A hearing before U.S. District Judge Alison J. Nathan of Manhattan is set for May 30.

Aereo’s technology works like this: The company rents space in a warehouse in Brooklyn and fills it with custom-made, wine cooler-sized computer hardware jammed with vertically aligned blades. (See photo.) Projecting from the blades are thousands of thumbnail-sized television antennas. These are tiny, modern-day versions of the old bunny ears that people have used to watch over-the-air television since time immemorial.

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Aereo then effectively rents each customer one of these antennas and all the other off-site hardware needed to operate her own individualized remote DVR using her Apple (AAPL) iPhone or iPad. As with most DVRs, the customer can choose to watch live (with a pause-function available) or watch later. The signal reaches the customer’s device over the Internet. The service currently costs $12 a month, and provides access to the 28 over-the-air channels one can receive at that Brooklyn warehouse.

It works eerily well, though at the moment it’s only up and running in the New York City DMA, or “designated market area.” That’s a funny story, too. Basically, Aereo uses FCC maps to determine the maximum perimeter around the New York City metropolitan area from which someone with a typical residential TV antenna on her roof would be able to pick up over-the-air signals from New York City. If the customer ventures outside that range, her phone’s GPS or wi-fi systems will eventually detect that fact, and Aereo will dutifully cut off reception. (So, for instance, some parts of the Hamptons get reception, some don’t.) Since it’s ordinarily not possible to receive New York’s over-the-air signals with an antenna beyond a certain distance, Aereo imposes analogous, if artificial, limitations on its users.

Legal precedents have already painted Judge Nathan into a weird corner. To the extent that someone uses Aereo for live TV, there’s a strong argument to be made that Aereo is illegal. After all, if Congress requires cable and satellite providers, like Comcast and DirecTV (DTV), to pay broadcasters license fees to retransmit their over-the-air signals—and it clearly does—why wouldn’t Aereo have to do the same? And if, for any reason, Judge Nathan finds that Aereo — the brainchild of engineer/CEO Chaitanya (Chet) Kanojia — is exempt from such fees, won’t cable and satellite providers just switch to Kanojia’s approach ASAP, socking networks and local TV stations with a huge financial blow? In legislation enacted in 1992 and 1999, Congress unambiguously expressed its intent that broadcasters be able to charge cable and satellite providers for retransmitting their signals.

On the other hand, to the extent that someone uses Aereo as a DVR, there’s a strong argument to be made that courts can’t lay a hand on it. There’s already a binding precedent — a 2008 ruling by the U.S. Court of Appeals for the Second Circuit, which covers New York — that seems to say so. The plaintiffs aren’t even challenging the DVR aspect of Aereo.

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So at first glance, if we take in the whole forest, it looks like Aereo’s live TV function — it’s key commercial attraction — can’t be legal, while it’s DVR functions probably are. In that case, we might think, Judge Nathan will just split the baby, banning Aereo’s live TV functions while leaving untouched its DVR functions.

Yet there’re two problems with that approach. One is logical. She’d be drawing a distinction between two process that are, according to Aereo’s lawyers at least, technologically identical. The Aereo technology works the same way, they claim, “whether the consumer operates it in the ‘Watch Now’ mode — i.e., playback at approximately the time the program airs—or whether the consumer waits until a later time to initiate playback of the recorded programming.”

The other problem is more practical, and seems like an obvious one, though neither side addresses it in its papers, and neither side’s representatives were willing to discuss it with Fortune. If Judge Nathan splits the baby, it seems like she would also have to decide how long Aereo customers must wait before starting their DVR playbacks. If a fraction-of-a-second buffer suffices, then the ban on live TV would be meaningless. If not, then any minimum court-ordered delay will seem arbitrary as a legal matter, though crucial as a business matter. If a 5-minute delay suffices, Aereo might still have a viable business. But if customers have to wait till their show is over, that might kill Aereo’s appeal.

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Here’s the legal landscape: Since 1976, the copyright law has generally forbidden unauthorized retransmission of over-the-air broadcast TV signals. These statutory provisions overturned two U.S. Supreme Court decisions which had found that cable providers didn’t owe broadcasters squat for retransmitting their copyrighted programs to paying subscribers, which Congress considered unfair.

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So the copyright law gives broadcasters exclusive rights over “public performances” of their works, and then defines those to include any transmissions “to the public, by means of any device or process, whether the members of the public capable of receiving the transmission receive it in the same place or in separate places and at the same time or at different times.”

Aereo claims to circumvent all that gibberish because it facilitates only “private” performances of TV shows, not public. “First, a consumer turns on a remotely located and individually assigned television antenna, accessible only by her, and tunes to the over-the-air television programming of her choice,” its attorneys write. “Second, [she] uses the Aereo system to make a unique copy of the over-the-air program, from the signals received by her antenna, and to store that copy in a remotely located DVR. Third, [she] uses the Aereo system to play back her unique copy to herself, and only to herself, on her Internet-enabled device.”

If Aereo’s argument ended there, I’m not sure I’d buy it.

But it doesn’t. In 2006, some movie and television studios challenged the legality of Cablevision’s (CVC) cloud-based DVR service, known as “remote storage” DVR. Not surprisingly, a federal appeals court ruled in 2008 that there was nothing wrong with a remote-storage DVR, which simply relieved customers of the need to make space for DVR hardware, like a TiVo, in their home.

Now again, at the 30,000-foot level, the Cablevision ruling seems totally unremarkable. After all, Cablevision was already licensed by the broadcasters to retransmit their live signals, so why would providing DVR services require still another license?

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But that’s wasn’t the stated basis for the court’s ruling. Instead, the court used language that seems broad enough to protect Aereo’s DVR service, too. In fact — and here’s the rub — the language seems broad enough even to protect Aereo’s live service.

The content providers’ main legal challenge to Cablevision’s remote storage DVR service was that it amounted to unauthorized retransmission of over-the-air broadcast signals, resulting in an infringing “public performance” of their works. The appeals court rejected that argument in these terms: “Because each [remote storage] DVR playback transmission is made to a single subscriber using a single unique copy produced by that subscriber, we conclude that such transmissions are not performances ‘to the public,’ and therefore do not infringe any exclusive right of public performance.”

That’s a great description of what Aereo’s DVR does, too. In fact, it’s a pretty good description of what Aereo’s live TV function does, also. See Judge Nathan’s quandary? Does she look at the forest or the trees?