Apple doesn't make the apps being sold in its store. Third party developers do.
If you insist on taking something simple and using an analogy, then a better example would be if Ford only allowed its customers to buy accessories for their cars from a Ford store... using the excuse that they can control the quality. Unfortunately it also means they can deny selling an accessory if it competes with one of theirs, or for any other reason they wish.
I guess you've never heard of the Big King (pretty much the same nasty burger). Any number of local burger joints have their own versions as well (nothing special about sticking an extra bun in there and putting Thousand Island mixed with mayonnaise on it). McDonald's burger is so small I don't know what the function of the extra bun is other than to raise the calories and carbs so you get fatter even faster.
So department stores and supermarkets should have no control over who is allowed to sell in their stores?
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Yes, but they're not Apple. So there.