> some number of them will see ads related to some conversation they had recently by pure random chance.

Or perhaps, they're just correlating the interests of people:

1. Person A reads about X online

2. Person A tells Person B about X

3. Person B sees ads about X, without ever having searched for it, concludes they're being spied on

I'm 99.9% sure WhatsApp does this, perhaps illegally or at least grey-area.