N.
I'm not sure what your legal rights are, but you could maybe do a couple things. First, are you using insurance at all? If so, you might consider contacting your insurance company and asking them if you're obligated to pay for a procedure that he didn't really "do" so much as it just "happened". If you're not using insurance, OR if you are, but they can't give you an answer, you can try to contact the American Dental Association, or whomever is "over" dental licensing and see if they can give you an answer.
I personally would tell the dentist I'm not paying for him removing the tooth when he did NOT actually remove it. It just fell out and he had nothing to do with it. I'd tell him I want him to take it off my bill 'cause I don't owe it. If he argues the point, I would let him know that I am contacting the ADA to see what my rights are. He might back off if he knows you're going to file a complaint. I would also wait to tell him this AFTER the rest of the work is done of course.
Again, I don't know if any of this is going to work, but that's what I would do in absence of any other sound advice.
Blessings,
N.