They own the infrastructure, but they do not own the device. The customer does. They bought it.
Apple comes along and says that anything you want to use on the device you bought and paid for needs to go through their infrastructure. That's where it becomes a huge problem. Not that they're charging for using their services, but because they're charging to let people do things with their property.
But they make it very clear that the iTunes store is the only authorized/approved means of doing things on the device, and try to make it illegal to do otherwise (although the Library of Congress put a temporary stop to that agenda). And while they don't go after the jailbreakers, they do try to diminish their experience with things like the iBooks jailbreak test.
When you combine this behavior and stance with the "charging through the iTunes store" policy, it becomes effectively a mostly successful attempt to charge for doingsomething with the device. The Apple Tax in isolation, while disturbing, isn't intolerable. It's when you combine it with their other policies surrounding the platform that the real problem arises.
BUT...
I don't disagree with apple in this one though, they own the infra and without them there would be no place to sell the stuff so you should pay.