Yep... you're right. I had forgotten that the Supremes had just let the Cablevision Second Circuit case stand and didn't rule on it themselves.
Wasn't their another remote DVR case though that they ruled on that had de-duplicated the data for multiple users? The difference in the Cablevision remote DVR being that they didn't de-duplicate data.
PART of the business model comes from a Supreme Court ruling (the Sony Betamax case) that permitted home recordings as fair use.
The other part is based on a Second Circuit case (Cablevision) that authorized remote DVR service.
There is a circuit split on several elements in the Cablevision holding so it is quite possible the Supreme Court could rule against Aereo.