According to public material, Google does not train Gemini on Gmail or Docs: https://blog.google/products-and-platforms/products/gmail/pr... https://proton.me/business/blog/google-docs-ai-scraping
You may well be right about Google not including the said data but your support for this point is weak.
Malicious acts from large corporations are certainly well known, but they're also grossly over-represented in the news and mindshare. Mostly things just work as they say they work.
I don't really know what proof you're looking for, it's well known that it's hard to prove a negative. I'm not suggesting taking Google (or anyone else) at face-value, but rather saying that when you think about T&Cs, laws, PR, etc, it's unlikely.