You're right, New Mexico being remote from central Mexico. Though not so much in Puerto Rico, the Inquisition was active in Mexico. Out in the boonies like what is now New Mexico, not much of a risk. But her story isn't like many you can easily find of people "finding" centuries old roots through mysterious practices. She says her ancestors moved to Puerto Rico to continue practicing their religion. I don't believe that.
You're right that couldn't have happened anyplace in the Spanish Empire after 1492 until modern times. Either she doesn't want to admit what her ancestors did after the expulsion or she's making it all up.