it is possible that the notice was prepared before the IRS recorded your payment. before going through the trouble of sending the IRS documentation I would check my tax account transcript or record of account transcript.
To register and use this service, you need:
your SSN, date of birth, filing status and mailing address from latest tax return,
access to your email account,
your personal account number from a credit card, mortgage, home equity loan, home equity line of credit or car loan, and
a mobile phone linked to your name (for faster registration) or ability to receive an activation code by mail.
https://www.irs.gov/individuals/get-transcript
