You can train models of all kinds without disclosing anything personal about a user. Also see differential privacy

“Keep in mind that, as a model running through DuckDuckGo’s privacy layer, I cannot access personal data, browsing history, or user information. My responses are generated on-the-fly based on the input you provide, and I do not have the ability to track or identify users.”

Training and fine tuning happens offline for LLMs, it’s not like they continuously learn by interacting with users. Sure, the company behind it might record conversations and use them to further tune the model, but it’s not like these models inherently need that