An actual example. When my second wife and I decided to divorce, I attempted to proceed with the divorce in the State of Michigan where we were married. Despite every attempt, it was impossible due to the State's residency requirements. However, due to the marriage being registred here in Thailand, we were able to complete the divorce here, which then has to be recognized by Michigan.
While a marriage certificate from another country would likely be accepted in other legal settings, such as property registration, etc., I suspect the Thai marriage certificate would be easier to work with.