I agree that it sounds very suspicious. But, I (having been a victim of the "any key answer" feature on my phone) can understand how it can happen that you can answer a call and not ever know you answered it. Of course, I am not saying that is what happened here. For example, I once picked up my bf's cell phone to see who was calling. It was his ex. He said he didn't want to talk to her, so I set the phone back down, not realizing that it was set to accept the call when any key was pushed. As I set it back down, I must have hit a key because she was privy to the whole conversation that we had about why he didn't want to talk to her right then. Embarrassing and just a little bit awkward.
However, I doubt that is what happened here, but there are ways to answer your own phone and not realize that you answered it. I do think that this is something much bigger in respect to this case. Maybe that is why they won't talk to LE anymore. Maybe LE said, ok, we talked to your phone company and they said you were all paid up, so can we please cut the crap about your bill not being paid and your phones not working? JMO.