Depends on where they are, how recent they were taught, I think. I went to an arts high school for jazz performance in the 90s, and we were taught Nashville number system, but we didn't often play songs from that kind of chart. The professor would use it for explaining progressions and turnarounds and such on the board, because it's very concise.
Roman numbers mostly came up in the traditional music theory lessons, they didn't often appear on charts we played from, either. We mostly played from charts from the Real Book (which usually are written in the recorded key and use named chords, rather than numbers). In college, it was all Roman numbers, but the school didn't offer jazz or popular music classes, it was traditional music theory.
Anyway, I think jazz players probably know the Nashville number system, but probably don't play from them often, unless they do session work or make their own charts. In the session case, they're almost certainly playing from Nashville number charts sometimes.
I think most jazz players play more by ear than from charts, though, and transposition of a memorized song is different from transposing from a chart. The reason the Nashville number system is so common in session work is it makes it much easier to transpose to a different key on the fly and see the relationships in a song you've never heard. It's also very concise. Roman numbers also mostly have the same transposition/relationship benefit.
I have seen jazz charts with both Nashville numbers and Roman numbers (but mostly actual chord names) above the melody, so I don't think anybody's really wrong here (except the person who thinks the Nashville number system is just music theory for dumb people, which completely misses the point). It's pervasive in Nashville, but it spread around the world since its invention.