Training off data you published for public consumption, e.g. pretty much user-generated content on social media, or anything publicly accessible on the web, is one thing. Training off private conversations is a whole different thing. I doubt any major company is doing the latter. Would be a PR and legal firestorm. Which doesn't serve the interests of companies training AI models either.
On the other hand, they are also very motivated to have a large mass of data to train their AI.
Which of the two motivations wins, is debatable. Today I'd bet on AI.