Yes- they are renting me an antenna in the locale the performance is being broadcast, and providing connectivity to that antenna. That is not a loophole- that is the letter of the law- that an individual can receive a broadcast performance of a work, but that it cannot be duplicated. It meets the letter of the law- unlike a system that received the broadcast signal, captured it, and provided the same copy to many users, which would violate the 'public performance' section of the law. Renting me an antenna makes it my individual private antenna, removing the public aspect of the performance, and making it perfectly legal.
It's the letter of a law written in the 1970s, when streaming technology like this didn't exist. No-one had even conceived of the idea that you would group hundreds of antennas together and stream them across a wide area network to users.
The spirit of the law as passed was to stop cable companies capturing and rebroadcasting over-the-air TV signals without compensation. So it shouldn't be too surprising that the Supreme Court made the judgement they did.
It's quite simple: when this law was created, was Aereo's use case considered? If the answer is 'no', then you can expect the law to be refined to cover it at a later date. Odd legal loopholes don't get to stand just because they've been around for a while.
To add to this, they didn't see a distinction between transmitting and performance, and felt the law was clear about the distinction between the role of the viewer and the performer. What was made clear was that one person could not hold both roles.
On if such a performance was private or public: the decision said that it was a moot point as the "commercial objective" of Aereo was the same as if it were public. The law as it stands did not intend to separate private and public performances.
"Oh, the law says no cars in the park but I'm driving my pick-up truck through the park! Ha ha, I win, I talked the computer to death like Kirk did on Star Track!1"
