I wouldn't be surprised if their privacy policy would say "what you send is private" and then it wouldn't apply to unfinished prompts on technicality
OpenAI’s statements in response to the Millenium Prize (and related) disputes I think are a pretty obvious example of this in practice. One man’s “user prompts” is not another’s “reasoning trace scratchpad”.
This comment by Falserum on the mathematics research post articulates it well: