I don't think anything was very surprising to me in the video - maybe because it was made for the police, so that it comes across as more strict to the general public.
I found this for more official info:
http://www.arb.ca.gov/msprog/aftermkt/aftermkt.htm
I don't know if other states do this, but in CA if you are putting an aftermarket part on an emissions controlled vehicle, the part has to have been approved by the ARB and will have an EO (executive order) number to prove it, so that it can be identified by inspections offices. Seems pretty straightforward to me - if you put an illegal (for off-road use only) part on your ('76 and newer? could be wrong here) car then you're breaking the law. I think if you don't submit to a search on your car for any reason then they can arrest/detain you.