Under the changes that Congress specifically made to the Copyright act I do believe the court ruled correctly. Congress moved in 1976 to protect broadcasters from Cable companies doing nearly what Aereo is doing, capturing and sending by another means the broadcast of a TV station.

Congress at the time did not like how the courts were ruling in favor of the then fledgling CATV services. Courts ruled that capturing and sending the shows to cable viewers was not a violation as were not acting as "performers". Congress changed that they were, effectively stopping cable from providing local and regional channels. Well Congress showed who was truly doing this by adding in all sorts of new compulsory fees for carrying local channels. So CATV can and in some cases has to carry local content and pay for it.

TL;DR

Congress changes to Copyright in 1976 at the behest of broadcasters versus CableTV is the basis for the ruling. The original broadcaster owns all rights unless otherwise assigned.