Just guessing, 'cause I don't know this case from Adam, but I think charby nailed this one. If they were giving content away, that's one thing. Selling someone else's intellectual property? That's not gonna end well for you.
It was an interesting case. Nick didn't get it quite right in my mind, though.
Let's go back in time: VHS and time shifting was determined to be legal/constitutional. Yes, the broadcast companies sued the makers of VHS and Betamax for producing equipment that 'could readily be used to violate copyrights'.
This resulted in a long line of history where the humble VHS recorder morphed into a digital video recorder. Anyways, so DVRs are legal. Leasing a DVR is legal; IE you don't need to own the box in order to record from it. It's been long tradition that you don't need to own the antenna - look at all the renters out there. Along with this, it was determined that a DVR that can stream to a remote location was also legal - see
Slingbox. End result is that you can location shift along with time shifting.
So, you can rent/lease the DVR and antenna and you can stream it to remote locations. Owning the equipment is optional. Now look at servers - virtual private servers have been a thing for quite some time. So it's logical to virtualize the DVR and put it in 'the cloud' where there's fast connections and lots of bandwidth to minimize delay and maximize quality wherever you might be.
So what aereo was doing was renting you a remote 'cloud' DVR with your very own(tiny but presumably optimally placed) antenna for recording. Every user's recording was unique, despite the massive space and quality savings you'd presumably get by using a bigger antenna and simply creating a master recording. Indeed, you had options much like standard modern DVRs for a mix of telling it what to record and it guessing what you'll like and recording that.
I have to say that, as a techie, I disagree with the ruling because it sets historical precedents on it's ear. To misquote George - 'Sellings legal, Sex is legal, so why is selling sex illegal?'.