This is absolutely correct. Offering a reduced sentence is one of the interview techniques I cannot do. Big no-no! After a subject writes out their confession there is a form that is read to them that they sign. One section says, in effect, “I was not promised a reduced sentence by the investigator”.
However I can say things like “hey, I’m just charging you with this. If I wanted to be a prick I could charge you with this, that, and the other thing”. Notice that statement isn’t a direct threat to charge you with other stuff or that I will if you don’t tell me what I want to know. It’s just a reminder of how nice I am not to charge you with all the other little things you did in addition to the big thing.
But none of is pertinent to the link in the OP. I don’t see any violation or illegal seizure in asking for a SS#. And until we find out what happens to those that refuse were kind of stalled in the conversation on it.