Provocative? suggestion: actually a bright, well-adjusted, well-motivated child with supportive parents would be just fine in almost (not quite!) any gifted magnet or rarified gifted programme in the US. The gifted programmes are just better education, full stop.
Gifted programs vary quite a lot, though. There's the one I was in when I was a child, which was something like once-weekly enrichment (maybe less). It was things like logic puzzles and cool science demonstrations. I had a French mentor for a while, which was fun. But I was not accelerated (though we were ability-grouped). Yes, any bright kid could have enjoyed and benefited mildly from this somewhat goofy program. Why not?
Then there's DD's gifted magnet. I think MOST kids with IQs over 115 (?? I'm guessing) could hack it with effort and given no LDs, but for some it might be quite difficult, and they would need a lot of parental support. Some of the kids in DD's class need a lot of support now. Note that my hesitations have a lot to do with the writing expectations (high) and the workload (heavy). Reading level is also expected to be high, though--no instruction in learning to read has been given at all, as it is assumed all students are reading above grade level on entry (in grade 2). Math also proceeds double pace much of the time. Science and social studies are at least a grade and sometimes several grades ahead (one curriculum DD8 is using is clearly intended for middle schoolers).
