I had this happen to me recently. I was speaking to a friend about a subject that suddenly started to appear in ads after I hung up. It was spooky. But I think it has more to do with the activities related to the people we know. I'm sure because of Android, Gmail and search they have a good understanding of our general association group. I bet my friend did a search on what we were talking about and Google was able to determine that others in the group would be interested in the subject. They don't need the microphone input. They have better (more direct?) ways to get the information.
What you described is basically how it works. You all get finger printed on the same network, finger printed on google searches, finger printed at the routers, and then associated. 6 guys get together for beer and someone brings up wood chips, 1 guy later googles BBQs, you're all getting BBQ ads for the next week and a half, the 5 other guys think the phone is listening to them because they don't know one of the guys actually googled or triggered something related to BBQs. I once knew my roommate was pregnant before anyone else because I got a bunch of ads for baby shit all of a sudden.
I actually believe the alternative theories are scarier than the phone actually listening to you. The one thing I keep hearing over and over again from people is that “I talked to so-and-so about this“ and now I’m getting a bunch of ads about it. What’s scary is that it knew you two were in the same room that one of you had a recent interest and that there was a likelihood you discussed it. That seems worse to me than just listening the conversations.
