I don't think that the issue is whether or not she owes him money, but how much she owes him.
She has to pay a certain amount of unreimbursed medical expenses before they have to start dividing the remainder. She feels that she has covered her upfront portion because she still responsible to pay the dentist. He feels that she should have to reimburse him in full a bill he covered, because she hasn't actually paid the dentist yet.
In the end, they are each going to be responsible for the same amount of money in either scenario.
I was trying to follow along with what the OP was posting and I saw the "she owes me $80" remark.
It sounds like OP's ex is playing games here expecting to just be handed $$ without proof -- or sitting on receipts for a long time expecting a $$ windfall.
I would suggest to the OP to send a letter -- certified with return receipt -- asking for all copies of the receipts, along with copies of all canceled checks/credit card receipts that indicate payment has been made & to submit it to him no later than 10 days from receipt & if they have not been provided in this time, then it'll be presumed she has NOT reached her portion. I would also include a copy of the paid bill with this as well.
This way, when/if it goes to court and she tries to dump a bunch of receipts expecting to bank, the letter can be presented as evidence that he's attempted to address this and was ignored.