Snopes is an Annenburg affiliated website. I don’t give any credence to that site anymore.
That being said - if the social security number was issued by a misrepresentation of the zip code, then the social security number was then mailed to a Connecticut address. From what I’ve heard of Connecticut back in that day, you had to personally show up at the office to receive a SSN.
The issue was whether the SSN was issued to Ludwig or not. That appears not to be the case based on the SS website. This is not to say that Obama is not using a phony SSN now or in the past. We just don’t have access to his records to see what SSNs he has used since age 16.