When I first started gardening in the olden days, our next door neighbour had two big eating apple trees in his vegetable garden. He rotated vegetables quite strictly and inevitably they all were grown at some time under the canopy of the apple trees.
It was a while ago but I cannot remember him having any less of a crop because of the trees. Having said this, he kept about 300 hens in his back garden and used the manure from the hen houses on his vegetable patch. This might have had more to do with it... Well the moral of the story might be that, if you are planting below a fruit tree, you need to add some well rotted chicken manure to get good crops.