SHCP/SAT links the permiso temporal to the individual's PASSPORT NUMBER and no other way.
Not returning the vehicle and permit within the 180 days opens up a can of worms you cannot believe, electronic bells and sirens go off in the Hacienda Aduana database system, and EVEN IF the vehicle is taken to the border later and holograms scraped off and papers surrendered and receipts taken (did I mention the horrendous fine?), folks have told me tales of woe in which hours-long delays were imposed (prohibiting passing into Mexico) while the tramites were researched in D.F. BY HAND to verify the infraccion had been cleared up. I am one of the unlucky ones. But now being a citizen I am not allowed to 180 day or 10 year permit a motor vehicle not even one with Frontera plates (Michoacan is not a Frontera state).