The airline personnel are not immigration officers, all they need to do is check that the ticket is correct, that the person's name, the name on the ticket and the passport coinside.
For a Mexican traveller, they also check that they are in possession of a valid visa to enter the US.
For travellers that are not Mexican Citizens they are requiered to collect the the visa issued to the person by the Mexican government, they do not check for Temporary Importation Permits (TIP) since the computer system that they use is property of the airline and is not linked to the inmigration system as of today, the assumption is that you entered by air and not by land.
So leaving the country is not the problem, returning might be where things can get nasty, so plead ignorance! you might get away with a fine and you might not get the vehicle confiscated, also leave the vehicle in a garage or RV park out of street sight.
navegator