alt Hacker NewsDisabling "improve the model" is one thing. Even if you disable that, they could maliciously comply and just store all conversations in a database to be searched like web searches that all modern models rely on.
Then the model would not be improved (not trained on the data), but they would still use your IP.
Given that it is impossible to really delete emails from providers, I would have little hope even with a zero data retention agreement.
My personal view on this is that there are enough people who need this to not be happening or who would be very happy to catch any of the major frontier model providers fibbing about it, that needles are constantly being added to the haystack and searched for in subsequent models and requests made to them.
Proof of training or RAG search on data that was private would be a huge smoking gun and would change usage habits overnight.