I'm honestly curious what is wrong with renting an antenna from a company and streaming the signal, regardless of location.

Your intent to figure out exactly where the line is drawn is a failure that geeks have when going about the law. The law isn't written for a robot to unfailingly interpret. You won't get a good answer for the same reason the tribes making headphones out of coconuts won't get a good answer for how exactly they need to wear them for the cargo planes to come back.

I think the court has found that the "distribution for pay", i.e. "Cable TV" aspects of aereo's service outweighs the "antenna rental" aspects, and that makes it charging for a public performance.

If you rent an antenna on top of the Empire State Building, digitize the signal, and set up your own means to stream it over the internet to your house in Peoria, that is probably a private performance. If you effectively sell someone access to the stream (like a Cable TV company), that is a public performance.

This is also what ESB would be doing by letting people rent antennas and streaming servers.

Aereo is selling streaming TV service that just happens to use antennas in the backend.

You might say, it's all the same in the end from a technical point of view. And you're right, but the law doesn't care about the technical point of view. From the legal point of view, Aereo is selling TV streaming, and must comply with laws for TV streaming.

Now, if the equipement were sold instead of rented, and obstensibly Aereo was only providing electricity to the antenna/DVR setup, then things might have been different (at least it was implied in the oral arguments). But obstensibly the service being provided by Aereo was one of broadcasting, not of hardware hosting.

I don't think you'd have any trouble setting up DJB's Internet-Accessible Antenna Rental if that's what you actually offered. Stick some SDR equipment on the antenna and give me access to the raw bitstream. If I want to watch TV with the service, then I can tell your equipment to tune to the appropriate frequency, and then decode the bitstream locally. But if you set up DJB's TV Streaming without paying any license fees, and you just implement that by receiving signals from an antenna, it's a different beast even if it looks the same technologically.

However, I don't think the two decisions are inconsistent. As I understand it, Cablevision was already paying license fees for rebroadcasting, and the case was just about exactly what they could or could not do with that license. Aereo's case is about whether they need to pay license fees at all.