To be clear, an H-1B visa is petition based so unless the CBP officer has reason to believe that something is amiss, the officer is not authorized to ask to see a copy of the petition; that clearly crosses a line. The TN is not petition based so every time a TN worker seeks admission, the CBP officer is authorized to re-adjudicate the TN application.
It's technically true that a TN may be reviewed at every entry true but I have personally crossed the border dozens of times with TN status and I know of many others that may live in Canada but have a day job in the US. It's a much easier entry vs. tourist/business visas. An H1B may or may not be petition based depending on your citizenship (e.g. for Canadians it's not) and either way any specific trip is either for business or leisure and certainly the immigration officer has authority to deny entry. EDIT: Sorry I misread that as a B1 or B2. H1B is different. Also much harder to get vs. a TN (which is just easy process at the border).
