The court opinion talks in terms of user interaction with menus on the site to select shows. We're kidding ourselves if this works anything like "hardware rental". If it were, it would feel more like AWS.
WTF
I can black box Aereo and it looks like a whole lot of manual work by me to set up an antenna stream and time shift recordings etc.
Aereo wanted to define the activity by drawing a box around the tiny antenna and the user.
The Supremes draw the box around Aereo and their customer base.
Edit: having read the decision, it seems there were companies that provided antenna services back in the 60's, and congress amended the copyright act to forbid them. The ability for Aereo subscribers to choose which material is transmitted is key to Aereo's argument.
Redesign their system to have discrete units. Aereo users would then buy the boxes (similar to that Hauppauge one linked elsewhere in this discussion) and pay a monthly service fee for power and bandwidth. If they are done with Aereo, they can have the box shipped to them for a small fee, or sell it back to Aereo.
The user will have complete and direct control of the TV box. Then there should be no problem.
Hardware costs will be higher though, and maybe the service ends up costing more overall. It would still be worth it for some people, like my friend who (while he likes sports in general) really just wants to see all of his favorite sports team's games from another city. I know of other people with similar use cases.