Yes, you are probably correct.
When I’m in America, and when people ask where I’m from, I initially say Scottish, so that they can relate to the accent, and also that they have a geographical idea of where in the UK I’m from.
From their point of view, they don’t realise that there are 4 nations making up the UK but see Scotland as a region like Yorkshire , Cornwall, etc.
Similarly, when I speak to Americans in the Uk, and I ask them where they’re from, they’ll say Florida, Michigan, whatever.