If you read the section Sec. 11 Corrected Returns, there is no indication that the NEC has to be corrected for inaccurate address. The only time an address has to be updated is if you did not receive the form, which you obviously did. The only other references is https://www.nctracks.nc.gov/content/public/providers/faq-main-page/faqs-for-1099s/faqs-for-1099s-Wro... which is specific to North Carolina, but there most likely are more if you search.
If you do want to make sure, you can send a request to the issuer to update the address, this may not be a bad idea so you will either have a copy of the corrected form or at least made attempts to correct the issue. Which state was on the 1099-NEC addressed to? I can look for specifics there too. @jb183
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