Would you avoid using Gmail and Google Doc?

When it involves the non-white hat SEO stuff, would you avoid using Gmail and Google Doc?

Personally, I'm a long time user of various Google services, but I've been thinking about the ramifications as I'm getting more involved in this stuff.

Am I being too paranoid?

Yes I would certainly avoid it. I would even avoid webmasters for that matter. You are not being paranoid at all.