The problem is that the legal definition of retransmitting doesn't include Internet point-to-point communication. If you have a Hopper or SlingBox or an "Advanced" DirecTV DVR that can stream your video, it could also then be technically retransmitting the broadcast signal.
The legal definition needs to open up to be technology free ... otherwise FIOS could retransmit any station anywhere without permission or payment.
What Aereo does is lease you a tuner+antenna combination and then allows you to access "your" antenna+tuner via the Internet.
That is the theory ... but there is a lot more shared resources in the Aereo model than with individually owned and operated antenna / tuner / recorder setups.
In theory, it would be no different for them to have 5,000,000 Dish Hoppers and receivers set up and allowed you to access "your" DVR through the Dish app (although this would violate Dish's terms of service, the technical and legal hurdle WRT the broadcasters would be the same.)
The broadcasters will NEVER be 100% happy with any arrangement where their signal is retransmitted. But looking at it realistically, "hosting" in the same market (not violating distribution rules and blackouts) would probably be permitted by the courts ... and a Sling / Hopper combination would have both the permission and payment that comes with a subscription to the service. The channels can charge DISH for such a rebroadcast. Aereo isn't paying the stations.
However, the courts have not ruled so far that using Sling or other technology to watch your DVR's programs from a remote location violates copyright in any way.
Other than the integration with some DISH products Sling is a separate product that is owned and operated by the consumer. In the battle over Aereo the broadcasters have attacked Sling (claiming that the rights they sold DISH to rebroadcast their signals to homes does NOT include devices outside the home).
I'm not sure how this case will end ... and how much of a landmark it will be. It has the potential to remove a lot of restrictions on broadcast retransmission or to add further restrictions. Stay tuned ...