I'm not sure the answer is correct on the information given.
You can deduct property taxes you paid that cover your period of ownership. In most states, property taxes are paid in advance, such as in January for the upcoming year. In that case, the seller would give you a credit at closing for the last few days of 2020 that you pre-paid but which they will own the home, and you have to reduce your deduction by the amount of the credit (the taxes that are attributed to the time you did not own the home.)
In a couple of states, taxes are paid in arrears. You would pay in January 2021 for the 2020 tax bill. In that case, when you sell at the end of 2020, you give the buyer extra money to cover the January tax bill that represented your ownership period. Those taxes are indeed deductible by you in 2020 even though you paid them to the buyer instead of the city or county.
It's not clear to me that is reason you paid the extra. Assuming it is, the expert's answer is correct. But if there was some other reason you paid a property tax settlement to the buyer, we would need to know more.
