I'm Webmaster for a district council and thankfully my website doesn't have adverts - it was only three weeks ago I last had to send an email listing arguments of why having adverts on our website was a bad idea as we are having to monetize anything we can due to austerity, and I'd used a scenario like this as one of the arguments for not doing so.
Fingers crossed I'm going to be able to bin Google Analytics too so there will be no cookies at all :)