Although this can be true, I find that when Americans say as much, it's because many of them don't understand our domestic arrangement.Andy, according to most yanks I’ve met British and English are interchangeable. In my view that means you can refer to USAians in whatever term you choose. I am British but I am certainly not English
Conversely, there are those who are from these shores who will say that they're British rather than English, for their own personal reasons e.g Brexit and some, will consider my declaration, that I am first and foremost, English, nationalistic with racist undertones so you can't win.
Like most people, I have no issue with Scots, Welsh or Irish, declaring themselves, primarily as such, rather than British when asked but somehow, when I do the same, it's often followed by claims of my having a 'little Englander' mentality (especially on sites such as this) and a self perceiveved, superiorty over all others............isn't that a racist stereotype?
I won't expand on my own thoughts on this any further for fear of annoying the Gods. ⚡⚡⚡