I trust the tool in that I don't send anything sensitive in there! Unless I built it, I assume it's going somewhere.
We have a policy at work around this where our most sensitive data can only be passed to on prem models.
That being said, I have no evidence of anything going to the cloud or frontier providers doing anything with chat history other than storing it for later.
Self-hosted + custom harness for anything I don't want getting out at all.