*But I can't see a situation in which Facebook turning on a mike to record conve...

But I can't see a situation in which Facebook turning on a mike to record conversations is not a huge violation of privacy.

Do they do that?

FYI, this is mentioned in the article. It also linked to this article on that specific issue:

Short version: It's not as simple as "they record all your conversations", but yes, they can and do turn on your phone's mic.