Objection to ID numbers as a concept aside, I don't think it actually solves the problem this author faced.
Fake identities are dime a dozen. It is not exactly hard for an illicit entity to just put some random ID numbers it bought off the dark web on its books. And now you have just made it even harder for the people who had their identities stolen to clear themselves. How do you convince some company drone doing sanction compliance that you didn't actually work for Sanction Circumvention Ltd when your ID number matches the one on their company's payroll files?
Not to mention the sanction list is full of foreigners. The American authorities compiling the list aren't going to know what's the national ID of a random Russian or Iranian guy running an import business. So what is going to happen if your name matches someone who's on the list with a blank ID field? Probably the same thing that happened to the author, I guess.
If they put an ID on a sanction list, there’s a possibility to verify it. They could verify that it actually belongs to the person they want to sanction before putting it on the list. Failing that, the actual person can prove that they don’t belong on the list by verifying their identity.
Verifying identity is a much simpler problem than establishing identity.