Mexican Insurance-
The issue is based on ownership. A vehicle that is financed, leased or rented is not the legal property of the you, the driver of the vehicle. You don't have legal ownership unless you have a pink slip listing you as the sole owner.
Recommend you just call the finance co. of your vehicle, as for a permission letter to take the vechicle to mexico( I had to have my letter notarized). They will want to know the exact dates you are entering and exiting Mexico. Buy your Mexican insurance before you get to the mexican border ( it is a zoo at the border). I used Vagabundos in Rio Vista, Calif.
IMHO, it is not worth the risk and potential for legal hasseles you could subject your self to if you are in Mexico without the letter of Permission.