The bottom half controls the genetic material in the seed, but the top half controls what the fruit will look like.

Yeah, that part isn't true. The top half has the sexual organs, and controls both the fruit and the genetic content of the seed. The seed of that tree will be a genetic descendent of the top half, not the bottom half.

The problem is, as the other commenter stated, that the offspring of the tree are not likely to share the specific combination of genetic code that makes the exact apple we are looking for. If you want that exact apple, you need a clone of the original tree, not a descendant of that tree.