Yes, we do. Mexico law was influenced Spanish rule & French rule. They were very homegeneous people and they didn't take to mixing blood, let alone adopting those not born of their blood as one of their own. They never adopted the feudal law of "jus soli" and to this day, they have one of the strictist immigration laws on the books.
Alright, then. On the basis of what you’ve written here and assuming that it is all accurate and confirmed to be so, I’m prepared to say that Mitt Romney is a natural born citizen and therefore meets that requirement for eligibility to the office of President.
A competent legal authority with no inherent conflict of interest would need to verify all this, in order for any such “vetting” to ever be consistently applied or to hold up over time, though. Popular opinion got us here and got us Obama.