I don't think it is really about "sensitive", but basically about any content you put in. Why would you give corporations your reasoning (data on how you interact with AI, how you "talk" etc.).
All of this is private, but not necessarily sensitive. You never know what is happening with this data. They might say they don't log it or don't sell it, then few years later you'll find it all online or read a book that has a story eerily similar to what you chatted about with GPT a year ago.
Although in this use case, it's likely because GPT guided you to write the same story as somebody else. Talking with an LLM about an idea is a great way to make it more predictable and homogenized. If you're fixing a bike or writing software, this is usually a good thing.
Gemini not long ago, when you said something "useful" said thank you, I will use it to help other users with similar problem. When asked "why would you do that, I thought our chat is private?" it would respond "Apologies. My mistake, of course this chat is private and your information will not be used." Funny.