Lol I'm not lying to you! I almost always hear an end-of-call sigh from the other person that I'm sure they aren't expecting to broadcast because they think they've ended the call, but nothing embarrassing yet!
I'll try to screen-record my next interaction and show you. I think the problem is closing the window shuts down the screen link but not the whole pairing session, but people don't realise they need to separately end the call.