I'd equate Adsense to old sweaty sticks of dynamite rather than plutonium. I take the horror stories seriously (not to mention the Adsense TOS) and never touch the sweaty dynamite.
As for accidentally clicking when highlighting URLS, in my experience, it's not even possible to highlight the URLS of an Adsense Ad (granted I'm usually working in Firefox and other browsers may offer different options). Of course, I'm slow sometimes and there may be some very obvious way to do it but given @littlecubpanda's experiences, it's probably not a technique that should be shared here. Clicking anywhere near an ad is living way too dangerously for me.
I'll add that putting your mouse near an ad is a bit like holding a loaded gun to your head. You can hover over ads in FireFox to see a tooltip popup of the URL but I highly recommend taking your finger off the trigger before doing so.