"Using a different source" is the problem. This isn't watching Directv through a Slingbox that you are personally subscribing to. In the AEREO case, Barry Diller put together OTA head-ends and server farms then sold subscriptions to them in various markets he had set up shop. This is technically an MVPD (just call it a cable company) that in current day business must pay retransmission fees to each and every program provider they carry. Like it or not, that's the way it is, and AEREO decided they didn't need to do that for all the reasons in the legal docs sitting with the Supreme Court. They lost..
So, yes, it IS illegal..