Re: But what if I choose to..
From reading the judgment, the court was of the opinion that:
(i) it had found cable television redistribution systems that used centralised aerials legal;
(ii) Congress had then legislated the 1976 act that made them 'illegal' (i.e. ensured they had to pay to repipe content);
(iii) the language used by the 1976 act also covers Aereo.
Primarily it seemed to hinge on the idea that since 1976 the mere act of transmitting a performance from point A to point B is itself a performance, and the test for whether a performance is public hinges on how widely the work is being distributed and the relationship between the various people that receive it, not on the specifics of each specific connection.
They may be individually recorded streams but they're all of the same work and the receivers don't know each other. So it's one work being performed to the public, and Aereo does not possess the rights to do so.
So my understanding would be that if you put your own TV on the web for you to watch you'd be fine because you're not performing to the public. If you invite your neighbour over then you're not performing it at all.
The full judgment is here: http://www.supremecourt.gov/opinions/13pdf/13-461_l537.pdf ; the summary is just the first four pages — then the lead judgment and the dissent are quite a bit longer.