Taxes are on the statement but not usually called an element of “closing costs”.
Closing costs generally are loan origination fees, deed creation, transfer fees, title search and title insurance fees, etc.
You need to look again on your summary and detail documents and say to yourself “credit seller” or “debit seller” and “credit buyer” or “debit buyer” at every line on both sides of the document. I think if you actually do that, you will answer your own question.
Next, as someone posted earlier, look at the Q/A about when the semiannual taxes are due. The first half was already paid by seller before the transaction date.
The second half is what we are debating here. Again, taxes are paid in arrears. You are billed in end of October for your December tax bill.
You and you alone are liable for the second half year tax bill. You must pay the whole second half bill even if you only obtain the house one day before bill is due.
So, the question is how you could have been charged-not credited-for the previous owner’s accrued taxes at closing. For that to have been a true happening, it would require that the previous owner not only didn’t pay what they owed you for accrued taxes but that you paid them the amount of their accrued taxes owed to you.
As Title Companies do this dozens of times per day, every day, I seriously doubt they would make such a huge mistake on their boiler plate documents.
I therefore believe that you have misread your summary documents and are not double paying for the portion of the tax liability that the previous owner owed.
As an FYI, I purchase and close 2-3 properties a year, and have done that every year for more than 10 years.
And have had the exact same thoughts as you several times but have always found answer in the closing summary documents.
The guy at the title company said that I would actually have a surplus in my escrow acct. My bank paid my taxes in October and I paid taxes in July when I closed.