I suspected as much, however that avenue appears all far too convenient. Even with a multilateral framework agreement as comprehensive as CRS, it's only as strong as the weakest link. If FIs don't authenticate the client's tax residency, then the whole system is underpinned by honesty through self-certification?Unlikely I would say, but they will ask for a Tax ID so with this they assume you are paying taxes there and have proper residency.
At least that's my experience with a reputable bank with good long lasting relationship.