The thing is, the constitutional laws are not a blanket statement; they do not supersede everything and everything. The way that one officer was saying how driving is a privilege and not a right; he's right and that is what makes those laws abide and not the constitution. It's also the reason why the TSA has the right to search you at the airport even if you don't consent to a search. The right to bear arms is not applicable in certain public buildings, etc etc.
The constitution does not apply in any and all scenarios.