You could say the exact same thing about Cablevision and their 'cloud DVR', but they won their case before the Supreme Court. Aereo was relying on that decision to enable a similarly inefficient system (1 antenna and DVR per subscriber) for broadcast TV.
I agree, and crazy workarounds like that aren't very nice either.
However, I don't think the two decisions are inconsistent. As I understand it, Cablevision was already paying license fees for rebroadcasting, and the case was just about exactly what they could or could not do with that license. Aereo's case is about whether they need to pay license fees at all.