I had a similar experience with fitting (done by Bob Murphy at ARB4U). I'd dialed it in pretty good to the point where he only lowered my seat about a 1/2 centimeter and moved my cleats even less than that. But then he got me on the trainer and put a laser level on my knee and said pedal. It was instantly clear that my knees were wobbling side-to-side on my pedal stroke and we were able to quickly try some insoles and verify the wobble was gone. Best bike money I've spent as well.

My condition was different than most people describe, which drove me to get a fitting. My knees felt fine on the bike, but I noticed when I was off the bike, they felt a little loose/wobbly. It was a very strange, disconcerting feeling that I'm happy to report disappeared completely a few days after the fit.