Well, that's just the point. Apple doesn't care about the quality of the application. They already have a screen for that by virtue of their control of the app store. They are refusing apps based on the technology that was used to create them. It could be the most beautiful, performant, amazing application ever written and their developer agreement rules it out.
Apple already has an extensive quality control process for iPhone apps. If they can't come up with objective criteria that they can test apps against in the approval process then they shouldn't just use prejudicial BS to try to filter out so-called low quality apps. It's anti-competitive and anti-innovative. It's nothing more than a big company throwing around its weight trying to be a bully.
In the Wal-Mart case you can hardly argue that Wal-Mart owns a monopoly on consumer good distribution.
The key thing here is that there is no way to get a legitimate application (and web-apps hardly need apply) onto the iPhone without going through the Apple channel. It looks and smells like a monpoly (at least as defined in previous supreme court rulings) to me.
Is it anti-competitive if Wal-Mart refuses to stock goods from a vendor who doesn't meet their quality requirements? If it were, all businesses would go out of business.
Apple isn't competing with Adobe. They are saying that they have quality standards for the ways apps are made.
It's as if Wal-Mart said to their (potential) vendors: Company X's factory equipment does not meet our quality standards. We refuse to stock goods made with Company X's factory equipment. So if you use Company X's factory equipment, we will not stock your goods.
This is hypothetical, but Wal-Mart does use its extreme leverage to get conformity of all sorts out of its supplies, including (believe it or not) by eliminating questionable agricultural production processes.
And, so far as I know, nobody has ever screamed monopoly about that.
By comparison, Apple does not keep the parts (XCode) or the instruction manuals (documentation) from their competitors. They are not withholding secrets. They do not lock them out of developing for the platform in compliant ways; they do not block them from cross-compiling to cacheable web app that can also be placed on the iPhone "desktop"; they do not stop them from loading their non-compliant apps directly, outside of the store.
They just will not stock their goods, in their store.
Now. Are there precedents of desirable retail stores being forced to carry products they don't want to?