No lawyer would take the case either. He eventually went to an identity theft company, who took $400 and fixed the issue in three months.
I use to work in Identity Management at a major university. A number of people came through our systems without SSNs. We had a complicated set of rules to make sure we didn't provision two accounts. We'd check if the names were reversed and we'd check both the month/date = date/month on the date of birth (people from other countries might enter it backwards without thinking about it). We even had rules for SSNs that were off by <2 digits with similar names. Every morning we'd have a set of "manual provisions" we'd have to stop and check.
Occasionally duplicate accounts get created and we'd have to go through a big manual process of combining them and telling them "You need to use this account; forget about the other one. It no longer exists," and get their stuff synced across all AD domains (Universities typically have several).
What surprises me about this article is the NYC system doesn't use the SSN (which is good in a sense, it should never be used as a identification number, see the latest GCP Greg: https://www.youtube.com/watch?v=Erp8IAUouus).
The idea of an identity and criminal record us that follows us digitally is a very new concept, one that didn't exist 150+ years ago; or at least no where near the complexity it does today. Immigration was also treated very differently. Most of are criminal background procedures in the US are plagued with problems like this; which is why most counties require fingerprint/criminal checks for immigration screenings.
Today, the idea of a national identification number is highly opposed in the United States. In some ways I favour this as I feel digital identities lead to a situation where people cannot escape their pasts. But it also means people use absolutely terrible ways to associate people such as name and birthday; totally non-unique fields that should never be used to identify people. SSNs offer no real security; no photos and your number +1/-1 is most likely a valid SSN of someone who was born the same day as you.