I don't know why the neighbor says it is not an apple, but it sure looks like an apple, looks like apple leaves, etc. Does the core of the fruit look like apple, does the flesh of the fruit smell like apple, do you notice any jelly/pectin around the fruit? The pectin is only seen occasionally, but could be confirmed with cooking this fruit down in a tiny bit of water.
The flowers will confirm it's in that family. There are many, many apples, and many, many crosses. Crabapple, lady apple, but absolutely some species of Malus spp.
I'm a very big fan of being absolutely sure of anything before you try eating it, but this is an apple with no doubt in my mind.