alt Hacker NewsPlayed trombone many years ago, but never well enough to ever adjust that finely (at least not consciously?). The tuning slide on the third valve on a trumpet usually has a finger fork/loop so that it can be tuned in realtime. I believe the first valve on higher end trumpets similarly has a thumb fork for the same reason.
I played trombone in high school, never very well, but I definitely adjusted like this. Actually, although it was a slide trombone, I'm talking about adjusting automatically with embouchure. Someone would play the reference note, I'd match (in 1st position) but bend my pitch to match. The band teacher once complimented me on the adjustment. Which was stupid, because (1) I wasn't doing it intentionally, and (2) the adjustment only lasted during tuning; as soon as we started playing, I was right back out of tune. I never did learn to suppress the adjustment so I could actually fix the tuning.
But with the way I played, I'm not even sure how much it mattered. The best tool for enhancing my playing would've been a mute. (And it would have been most effective lodged in my windpipe.)