My understanding is that that warning applied to the card itself, not to the number. That is, the bearer of that card has no provable relationship to the social security number on the card as it contains no attestable information (like a photograph or general description) so the card cannot be used for identification.

The number itself is of course used for identification from the beginning as a unique identifier for your "account" in the social security administration.

> In order to make Social Security work, the government needed a way to identify every single worker and keep track of their earnings every single year for the rest of their lives.

According to the article it seems that it was intended to be used for identification, just only for one purpose.