Whether they own the store or not has nothing to do with it. It's a straightforward legal claim. They have sent the same kinds of notices to app developers for other trademark owners. It's especially straightforward because they have published their own app with that name, so it's not just a matter of over-zealous trademark protection.
As the gp said. A trademark dispute is not necessarily a straightforward legal at all. Buying the claim of one side and using your power to enforce an otherwise tenuous sounds like ... uh bullying.
Apple has enforced the (unregistered) trademark of a fellow indie game developer the same way. Documentation was provided, the other party changed the name of their app, and everyone continued on their way without tears or lawyers. All quite civil if you ask me.
Would they enforce the indie-game developer's trademark if it were against an app that was: 1) not a game at all; and 2) came out a year before the indie game of the same name? That seems to be the case here--- Apple is claiming a trademark case against an app in a different genre than its own "Facetime" application, and which came out a year earlier.
Sometimes trademarks don't matter much and everyone can happily and informally settle the question. But it quite possible for a given trademark to be the main asset of a small business and thus when a larger business can happily use "informal" methods to take possession of that trademark, it would qualify as bullying - if you can get away without lawyers, it's actually worse bullying in this cases since you don't need any legal standing.
I don't know the exact story here - I'm just reacting to a claim that Apple informally deciding everything is inherently fair.
Given the general level of discourse (and lack of historical knowledge) around here these days, you'd probably be better served by adding some kind of sarcasm indicator. :)