I went to public schools and took orchestra, and the orchestra teacher gave everyone a private lesson every week at some appointed time. It was part of the curriculum I think.
Twenty years later, my two daughters went to public schools too, one was orchestra, one was band...and again, both got a free one-on-one lesson from the teacher each week during school hours. None of these public school were 'affluent', just average public schools I'd say.
I can't tell you if the same setup is still going on now that my daughters are around 30.