Yes, but of course there would be a Stars and Stripes U.S. flag waving there at the United States embassy in San Salvador, where I went to apply for and got my Social Security card. Where else would I get that if not for the United States embassy? So much easier to apply to colleges with an S.S. number to my name. So obviously there is nothing wrong with having a U.S. embassy nearby when you need them, even if we are not exactly employees of the foreign service in the governmental meaning of the term.
Coincidentally, one day while working in California, a Mexican person took note ot my Social Security number and commented that he had the same prefix, and that his number had been obtained from a U.S. embassy in Mexico. Oh, well, that was an interesting point that I had never thought of before. And even so, so what? Clearly my birthplace being in California, I am a native born U.S. citizen, never mind about the little glitchy S.S. point.