Should could have two meanings (at least).
Should, under the law, have Roy cooperated? No. We now know for a fact that the officers had zero RAS, that the stop and the subsequent searches and seizures were illegal, and that the officers violated Roy's rights.
Should, as a matter of practicality, have Roy cooperated? Yes, to an extent. At the moment of a stop, we have no way of ascertaining whether a stop is lawful or not. If we assume it is unlawful and it turns out not to be, we will end up committing a few process crimes, even if we are not guilty of any underlying crime. Innocence of the underlying crime does not mitigate process crimes. Just ask Martha Stewart.
If we assume the stop is lawful and it turns out not to be, we end up having said more than the law would have demanded. However, if we are careful enough to assert that we consent to no searches or seizures, then the inevitable continued hole-digging by the cop can be resolved later in a court.
In Roy's case, he initially assumed that the stop was unlawful, but later gave in to doubt about his perception. He was correct from the get. The stop was unlawful. If we assume that the stop is unlawful, and it turns out to be so, then we have (luckily) ended up in the same spot as the second scenario, and been spared having to identify ourselves. meh. Giving one's name, address, and DOB will make you look better on the tape. You are cooperating to the extent required by the law and doing not one whit more. The cop comes off looking like a demanding thug.
As I have said before, try to end the encounter. Failing that, act as though it is lawful, but no lagniappes! The officer gets what the law demands, a stern warning not to take one iota more, and nothing else. Not even a lesson in the law--no matter how badly he needs it.
JMO