Well, in blues, heavy metal, hard rock, etc. the distortion is often INTENTIONAL. That must seem right to you, yes?
In jazz, organ jazz, with the best players. . . I would think it is also most often intentional. Wouldn't you think that an accomplished, working, touring, recording organist would KNOW when his equipment is failing, or a recording engineer when he's overloaded an input, etc.? I would assume intentional more often than not.
I really LIKE the sound of distortion mixed with clean sounds. I'm guessing you don't. It's a nice color, it's part of drama.