I don’t even play a lawyer on TV, but if you willingly buy an SS (which if you’re legal you get free from the government) and use it, how can you not know that what you are doing is illegal? Your intention is to defraud your employer by giving false information as a condition of employment.
The point of the Supreme Court decision is just that; a person whose intention is to defraud an employer is guilty of fraud, but not necessarily guilty of the specific crime of "identity theft".
It would be similar to having a prosecutor convict somebody of speeding because they double-parked. Both are illegal. But you have to prove the crime charged in order to deserve a conviction.