You might be able to get two stay credits if you have a day rate (for example at an airport hotel) and then stay overnight at a different hotel, presumably arriving late in the evening at a different airport. [However, a day use room might not lead to a night credit. IIRC this is how SPG handles the situation.] If you pay a regular night rate but only use the room during the day or pay a full night to guarantee early check in or a very late check out, again you legitimately might be able to count the same night elsewhere too.

My personal attitude is that if the credit is questionable, you don't want to count on it for requalifying for status, while if you don't absolutely need it for status, then it really doesn't matter. For attaining a new status level during the year, I can't see Hyatt later trying to claw back benefits that were previously used, such as sending a bill for a Diamond breakfast that was consumed after your account was erroneously upgraded to Diamond. In these cases, most people would do at least one additional Hyatt stay before the end of the year to enjoy the new benefits, so that they would have a few excess stay/night credits in case they're needed. Again, IMO it would be wise to arrange this if it doesn't happen naturally as the end of the year approaches.