For me, it's a Bulova albeit one made apparently by Heuer, in the same way I see an early diver as a Heuer rather than a Monnin, although Monnin supplied both the dive watch expertise and manufacture. I wouldn't necessarily classify it as a PMH though, we usually use that term for the more off-brand watches. It would be interesting to see if anyone could find a contemporary Bulova price list to see how much it was being sold for - we have that information from Heuer price lists.

Scale it up to cars and it's not quite as clear-cut for me. Dropping a Ferrari engine into a Lancia Thema doesn't make it a Ferrari, but I still think of the Aston Martin Cygnet as a Toyota iQ (and a bit of a joke). So there are some exceptions, some re-badging exercises that don't go far enough perhaps. But if a manufacturer uses another manufacturer's watch to extend their brand, or add something not currently in their range, I would still tend to see it as the customer brand's watch. It's a bit of a cognoscenti's question too - to the layman, they will take it at face value that that is a Bulova and not even think to query whether it had been made by Heuer.