Our take has been that if you are working with one of these large companies, you cannot expect anything to be private. We've worked with a smaller more focused product where we were able to negotiate the necessary controls
Either it needs to run on our hardware, or we need explicit contractual guardrails around use of the data for their purposes. Obviously anything you give Anthropic etc. is going into their training pipeline for instance, and they change their terms of use every week so it's impossible to work with as a small company with no leverage