Crossing the border, at least at Nogales and Sonoyta, we have never been asked for any proof of visas for ourselves or permits for the vehicle. Yes, last year we crossed 4 times, in both US and Mexico plated vehicles and no one had any interest in us when we entered Mexico. The US? Passport please.
We got our Permanent Residency and still really needed to bring the RV down one more time with "stuff" in it and live in in for a month while the house was being made habitable.
We considered many things, including me (this RV 10 year permit was in his name) getting a new passport, which generates a new number, which would not be in the records, and getting a 10 year permit on it with my passport and a FMM 180 day visa. In theory there would not have been a record of my Permanent Residency linked to that passport number. Didn't do that.
Spoke to two attorneys here that know us and supposedly know the law. One said we absolutely couldn't legally drive a US plated vehicle no matter what it was or what kind of permit it had once we had our Permanent Residency.
The other said that "definitely" because we already had a 10 year permit on it that was issued before we got our Permanent Residency, we would be OK.
Both stated the opinions that the chances of being "caught" were very slim because other than the PFP, chances were very very good that no one else would actually know the rules.
No matter what, without a current FMM, the 180 day visa, the insurance is not valid. We had a claim several years ago, and the first thing they wanted was proof that we were in the country legally and as a tourist, not a resident.
So, what did we do??? We just drove down, did our thing, and drove out 6 months later, not bothering to turn in the 10 year permit because we were selling the RV and now owned a Mexican plated vehicle and have no intention of ever returning to the US.
The couple driving the US plated vehicle with Permanent Residency status very likely will not have any issues. When are you ever checked for your visas and vehicle permits? However, if they ever try to use their insurance, they will find that it is not valid, and they not only wasted their money on the premiums, they have a serious legal issue to take care of.
It would be very easy, without the correct permit/license plate agreement with just a minor accident to have the vehicle seized and be permanently expelled from the country AFTER handling the monetary issues involved in an accident.
When you sign the pages for your Permanent Residency you agree to follow the laws of Mexico or you will be expelled from the country and not be allowed to return.