Not really. They rented you exclusively an antenna at their location, and you can use it to watch over the air TV. There was no rebroadcasting technically, which is how they hoped to get around the law.
That's the only difference between Aereo and the original CATV companies. Original CATV was one giant antenna on a hill piping the broadcast to homes that couldn't get the signal; this is thousands of antennas intelligently provisioned on a hill piping the broadcast and providing DVR functionality to homes that don't necessarily want to deal with using the crappy tv antenna -> computer hardware available.
