Google is definitely trustworthy. I think Etsy is more concerned about unknown and unqualified third party applications that may be phishing for your information so they can spam you, or even engage in identity theft. Google is NOT that kinda business, I can assure you.
You can create a separate google account just for your analytics if you're at all concerned about linking your existing gmail account with analytics. Google doesn't care which email you use to set up the separate account, as long as it's a confirmed email address.
So you could make a completely new gmail account, link it to the new analytics account and keep everything separate. You can even have the new email account forward to your old gmail so you don't even have to check your new account (if you're lazy like me lol!)