At the risk of sounding like one of those open-source crazies... Mesa drivers will NEVER do this to you.
We argue over whether or not having an app hacks system in a fully open driver is sufficiently transparent. Don't want that driver hacking around games behind your back!
The notion of scraping your web history in a GPU driver would never even occur to us. If someone ever proposed it, it'd get NAK'd so hard they'd be feeling it for a year.