Probably not much help for your problem but I also get occasional problems with totally innocent websites.
Mostly it's a plant or re-direct type problem looking for me to buy something
I suspect that the innocent website (with cheap virus potection) has been slightly hacked.
The real danger to me is now clicking on those links that try to get me to buy something I wasn't looking for.
PS I never try to improve my ability to view something by clicking on something in the site that asks for it. Figuring if they can't make it simple to match my quick scan than forget it.