I have to admit I have never heard that an antenna causes interference in another antenna if it's close to it.
We like it when the forum is educational.
Those of us who deal with antennas on a regular basis may take our knowledge as granted. The antennas I dealt with were normally half or full wave spaced.
Trying to have two adjacent antennas receive different frequencies with each antenna tuned for it's own 6 mHz band (as Aereo claims) without adjacent antennas interfering can be a problem. If Aereo organized its antennas so that all of the antennas receiving the same channel were in the same bank of antennas they could avoid interference. But then you're back in the situation where the antennas are acting as an array - losing the independence of each antenna.
Personally I do not believe the broadcasters care if the reception technology is real or not. Aereo could install full sized omnidirectional antennas connected to full size tuners and digital encoders to feed their customers and the stations would still object to the commercial rebroadcast of their programming.