I don't know why The Time Traveler would say that about not becoming involved with anything in Mexico? There are many great places to stay in Mexico. VanX and T-Dot would, I am sure, agree.
One good thing about the Mexican timeshare account is the end date of the contract. US based contracts are "forever", unless you sell, die or default somewhere along the years of ownership.
The Mexican timeshare has a beginning and an ending date. It is RTU (right to use), no ownership.
What you need to know is how many years are left on the contract and how do you get your name on that contract.
I bought resale Mexican timeshares back in 2007 with years remaining on the contracts. I paid a closing company to transfer to my name. I paid the resort the fee to make the transfer. As D-Dot mentions that could cost thousands of dollars, especially with the "newer" contracts where timeshare companies dramatically raised the price to change the contract owner's name.
That fee by the company to transfer the contract into your name should be written in the original contract.