Good Ol' Boy No. 2: (soon-to-be former owner): Yep, got one on the hook. Now, remember: If she comes over to talk with you for some reason before closing, don't say nothin' about those damned roots and keep your car parked over the cracks.
Good Ol' Boy No. 1: Got your back! We been neighbors for 20 years, and you've been good enough to stay quiet about that, er, thing. So I'll wait 'til the new owner gets in, just like you asked. My bet is you ain't gonna mention those big ol' roots in your disclosure.
Good Ol' Boy No. 2. I been awful forgetful lately. (Laughter.)
Wife of Good Ol' Boy No. 1 (overhearing): Now, boys, isn't that fraud you're talking about? And just what was that 'thing' that happened?
Creative license, perhaps. But it seems a strong likelihood the old owner and your newly observant next-door neighbor were in cahoots in concealing the problem until you took occupancy.
In fact, if you can prove the neighbor broached the subject with the seller before you bought the house and the seller didn't note it on the "Seller's Disclosure," you'd likely have grounds for legal action against the old owner -- that is, if your neighbor persists on demanding recompense.
What (or who) is the nuisance here?
While it's true that invasive roots affecting neighbors' properties are legally considered a "nuisance" or "encroachment," the "when" and not the "how" in this case strongly suggests you aren't at fault. Could you have known about this? Maybe. But even if you hired an inspector before buying -- always advisable, by the way -- the problem may not have been apparent anywhere on your property.
What to do? First, I suggest you politely but quickly ask the neighbor if you can photograph the damage, for "insurance purposes" perhaps. Or just take a shot from the street if need be. This is so you'll have a record of the advanced stage of damage should your case ever go to court. A judge who is accustomed to such cases and sees such damage may not buy that "sudden root invasion" story.
Then write the neighbor a letter -- or better, have an attorney write one -- stating the damage certainly must have been evident well before now. Tell him that you're willing to overlook his collusion with the seller to illegally obscure that fact if he drops the subject.
Think of ways to get along
You could also mention that while you owe him nothing, he is legally entitled to sever the root at his property line if done in a manner that won't kill the tree -- ideally in consultation with a tree expert. You don't want that tree falling on either house.
This whole scenario, of course, is contingent on whether you're willing to get off on the wrong foot with your neighbor. While I hate to see this kind of rift, remember that this guy seemed intent on sticking you with a whopping bill from the outset. That's not exactly the welcome wagon. I'm betting he'll back down and I'm also guessing he'll be none too happy about agreeing to do the bidding of his old neighbor, who should be the real litigation target.