As a law student, I think both of these are defensible positions, and neither approach bothers me. I like the result as a policy matter, but don't know enough about the precedents or the Copyright Act to comment on the result as a legal matter.

TLDR of the opinion for the rest of HN:

"Public performances" are subject to copyright protection. The Copyright Act says: "To perform or display a work 'publicly' means to transmit or otherwise communicate a performance or display of the work to a [public place] or to the public, by means of any device or process, whether the members of the public capable of receiving the performance or display receive it in the same place or in separate places and at the same time or at different times." That last part was written specifically so that cable companies are engaged in public performances (three boos for Congressional idiots who write laws specific to one technological era and then don't update them).

The majority says because that sentence talks about public transmission, it implies there's such a thing as private transmission. And transmission of a unique server copy to a specific customer is a private transmission. (See pp. 29-30.) They think this case is about a "rooftop antenna [that] is rented from Aereo and its signals transmitted over the internet."

The dissenter says that "public performance" includes any stream whose fundamental purpose is to retransmit live TV to a large audience. And that's what he thinks Aereo is doing. (See pp. 49-50.) He thinks Aereo is functionally doing the same thing as a cable company, and that "Congress made clear its intent to [cover] ... 'all conceivable forms and combinations of wires and wireless communications media,'" so it doesn't matter whether there's a private copy on the server or not.

(Link to opinion: http://www.ca2.uscourts.gov/decisions/isysquery/82dcbc3a-986...)