If you are asked to provide your SSN and you ask "For what purpose?" and the requester lies and says "So I can choose my lottery numbers", it's not clear that you have broken the rule by revealing your SSN. However, perhaps the requester is breaking the rule (and perhaps they should know the rule, assuming they have a card themselves) in this scenario, but it's also not clear what action they would have to carry out with the SSN in order to have used it "for identification".

For example, if a system designer uses SSNs as a primary key in a database, they can claim that's just for simple indexing, and that they are still using name and address or photo to identify someone. A system designer could also claim that they were only using the SSN as a (weak) "something you know" factor (among many other factors) in authentication, which may not amount to using it "for identification". Asking someone their date of birth (to be checked against another source, or on a later interaction) doesn't mean that your date of birth identifies you, since millions of humans share the same birthday.