It has nothing to do with the technology. And the law governing copyright and broadcast rights has been pretty clear for a long time. It would be no different than my neighbor on the hill that gets great OTA reception capturing those broadcasts, running a cable down to my house and charging me to "watch" signals he captured. He wouldn't have the rights to transmit that copyrighted broadcast/telecast unless he went to the networks and got a written agreement.
Or let's say he has a big radio antenna and can get radio broadcasts from say KMOX, then retransmits that signal to an FM frequency of his choosing. (Yes I know FCC licensing and all that, but let's ignore that and just look at the fact that the technology doesn't matter) He'd need a license from KMOX to retransmit their copyrighted broadcasts. Ever listen to a baseball game, especially on the Radio? Somewhere around the 5th to 7th inning I grew up with Jack Buck or Mike Shannon saying: "This broadcast is presented by the authority of Major League Baseball and the St. Louis Cardinals, LLC. Accounts and descriptions of the game may not be retransmitted or broadcast without prior written consent of the St. Louis Cardinals, LLC. And there is a such thing as the "Cardinals Radio Network" in which smaller stations away from KMOX retransmit KMOX's broadcast of the game on their local FM or AM frequency. But they have a license to do so.
Aereo is no different. You are just replacing radio waves with the internet. Technology for delivery is different, but the legalities are the same. That's why the Justice is saying that it shouldn't have a chilling effect on technology. If Aereo had a license or got a license from the broadcasters to carry their stream over the internet, then no harm no foul.