The timing sounds like RF interference. I worked in TV a while back, and we were not allowed to have any cell phones (even silenced) on set - they would introduce this crackling sound into lightly-shielded cables near them. The interference would kick in about a second or two before the ringing started, because there's probably some handshake/setup before the receiving phone decides it's actually an incoming call.

In that case too, sending calls didn't trigger the interference, and neither did picking up the received call.