Honestly, it would not mattered if you cited 100 supreme court cases; the cop has his belief and that's what he is going to act upon (and why not, right?). And other policemen who may know different? Mums the word, wink wink.
After all, its just the one policeman's butt on a sling, not theirs.
Looks like they intimidated you into not recording but in this case, the only thing you would have recorded was your own arrest...if you are willing to go that route, go ahead. You would be in the right.
I've had cops tell me I cannot do this or I cannot do that; if I believe I am correct, I don't argue with the policeman (he has his own opinion & I'm not going to change it), so I just ignore the police & continue on.