I have had a good native Korean friend quite innocently (although randomly) point out that although I rarely make syntax errors I don't speak idiomatically at all and make weird constructs sometimes. Which makes sense, given my almost 2 years of study, but I would never think of saying something that to any ESL learner.
The same friend said something along the lines of "I talk to you a lot, so sometimes I speak like you [non idiomatically/weirdly] with my [native] Korean friends haha".
??!? was my initial reaction, but then I remembered that it's quite rare for a foreigner to actually learn Korean at all, let alone to intermediate+ levels. Internally I got reminded that I will practically always be a foreigner, though.
We're so used to people learning English and using broken English in all manners of dialects that it's not even a blip on our mental radars.