This was not my experience. Granted, it was a while ago, and I'm not sure I'd call myself "gifted," but being ahead of the rest of the class certainly didn't get you any time to do interesting things -- it got you a pile of busywork and angry glances from the teacher for being such a pain in the ass.
I doubt things have changed much; if anything, due to increased student:teacher ratios, I suspect they've gotten worse. I don't have any kids but if I did, I'd be far more concerned about a particularly bright one being wrecked by public school than I would a special-needs one who lagged the rest of the class.