During the time of the "Great Polygamy Purge", U.S. citizens who moved to Mexico or other countries in order to avoid polygamy charges were subject to extradition. The Edmunds–Tucker Act clearly stated those practicing polygamy faced a fine of $800 (about $20,000 adjusted for inflation) per individual and imprisonment up to 5 years. The Romney family faced at least a $40,000 fine. That is why so many of these individuals gave up their citizenship.
I find it highly unusual the Romney family would have risked felony charges and a hefty fine to remain U.S. citizens living in Mexico. It defies logic and the normal actions exhibited by other mormons during this timeframe.