I'm an American who spent several years living in the UK, and I agree with you both. You adapt quickly to asking for the loo (or the ladies' or the washroom or something like that if you personally feel silly saying "loo" or "lav") because the bathroom is something specifically else. My visiting dad once asked a waiter who'd come to pour water if he'd mind leaving the pitcher, and the blankness of the waiter's look convinced me to translate: the jug. (Which he did leave at the table; he may also have been surprised by the request itself, but in the moment it was clear that he was bumping up against "pitcher." Maybe it sounded more like "picture" to him in my dad's accent? Who knows.) BUT using local terms never made people believe I was a local myself. And I never did manage to get used to saying "tomato" with the low /a/.