I think this is key "To redistribute this content to users". The redistribution is not that far from what's currently OK right now, though. Is it illegal (right now) for one to record (using an antenna) on to a TIVO and then to watch said recording over the internet for yourself?
There is 1 antenna per user. There is 1 recording per user (Aereo is not recording a single instance of desperate housewives and then muxing that out to everyone). It is over the network.
Other than not owning the means of reception and means of storage, I don't see much of a difference between this and in home recording.