It's possible that the "lose $1M before I give him $10k" schtick is bluster. If you're facing a fight with someone, then convincing them that you're crazy, and that you're prepared to risk everything to beat them, might make them run away.
Incidentally, can you invalidate a patent, so the troll can't use it any more, if the troll declines to defend the patent? Can they just walk away, and then assert it against some other mark?
Yes, that's my understanding too. But if the party asserting the patent decides not to defend it, and drops their claim against you specifically, can you go ahead and invalidate the patent in court? If you can, and there's no defence, then presumably the patent is invalidated by default.
But it seems rather odd; in normal civil proceedings, you have an adversary against whom you allege some kind of wrongdoing. Who is your adversary if you are attacking a patent that nobody cares to defend? Can you bring a case against the patent itself?
I understand that in parts of the USA, the police can sue a car, a house, or a sackful of cash, so it's not beyond reason.
If the filed a suit against you, you can counterclaim the invalidity of the asserted patents. And even if they drop the claims against you, you still have the claim that their patent is invalidity.
If they just threaten you, can still sue the patent owner for a "declaratory judgement" that their patent is invalid, though you have to show harm in order for the court to hear the case. So if they promise not to sue or your customers, the case may get dismissed.
You can always file an Inter Partes Review at the patent office to attack any patent.
Incidentally, can you invalidate a patent, so the troll can't use it any more, if the troll declines to defend the patent? Can they just walk away, and then assert it against some other mark?