In my time abroad, I've become good enough at Brazilian Portuguese (my 2nd language, learned as an adult) that people in Portugal, where I've been living, often think I'm from Brazil. I always mention quite early on that I'm from the US but, nonetheless, I'm still intrigued with the idea of disguising oneself.
Linguistically, I'm highly doubtful that one can reach C2 status (that is, consistently sounding like a native) in a second language learned as an adult. Of the Brazilians I met in the States, I paid attention to how old they were when they arrived stateside, and judged their cultural/linguistic knowledge with people who were born in Brazil and never left. Anecdotally, I found the age of assimilation (of their home culture/language) was around 16. That is to say, if they arrived in the US at age 14, for example, they'd turn out to be more American than Brazilian by their early 20s. But I wonder how that can be entirely true if I myself don't seem to fit in that box, regarding my American qualities.
What was bizarre to me was that it seemed like no one ever pegged me as an American. IIRC, I was on an American military base when someone asked me if I was French.
So this didn't just happen out on the streets of Germany. This happened in spaces where you should by default be assuming that most people there were American.
Granted, a lot of soldiers married foreign nationals, so it wasn't quite that simple. I mean, my dad was a soldier who married a German woman while he was stationed in Germany. But it seemed to me like the guess as to my nationality should skew towards American when I was actually on an American base and not, say, fluently droning on in some foreign language.
Saw your comment about the military base so there's probably more to it than that, but the base probability of "american" in a lot of places is low.
But the first incident that stuck in my mind was when an American soldier greeted me in German on the sidewalk in front of the McDonald's across the street from the entrance to the American base. I had my very blond baby with me. Yes, I'm half German. Yes, my child is one quarter German.
But he was an American and Americans walked across the street to the McDonald's regularly. It very much weirded me out. Like "Why would you think I'm a German national? You're not. Do I not look American to another American on the sidewalk across the street from the American base??"