Oh, absolutely. I'm not saying that a professional musician at a major symphony doesn't know about theory -- this guy I took out was clearly very accomplished in his field and went to conservatory for it. Even the classical education I had up through high school included harmony and chords. But there is a difference between knowing the theory from a technical perspective to be tested on, and completely embodying it and using it to make music. Here's a recent video of my friend's group playing [1] -- everyone involved has a world-class level of understanding of theory, but uses it to improvise, not just to read sheets.

And let's not forget that a lot of 'classical' musicians back in the day were expected to be able to improvise as well. There's just a different priority for a 'classical' performer these days and a 'jazz' performer.

[1] https://www.youtube.com/watch?v=Y_BE_gi4YkA