I don't think the problem is that apple is trampling someone's "rights". I think it is more that apple is just continuing to act like a dick. (Whcih shouldn't be a surprise, since the dickery of Steve Jobs is well documented.)
I can't speak for others, but my personal beef is that apple is putting restrictions on the development process instead of the result.
I have ZERO problem if they want to put restrictions on the result. "Your binary must adhere to these rules, and behave thusly." That's fine.
I take great exception if they say how I can make it though. Saying "you can't use these tools" is silly. They shouldn't care what tools are used. To me, saying "you can't submit anything that was written in flash" makes exactly as much sense as saying "You can't submit anything that wasn't written by someone with blond hair."
(And yes, I'm equally insensed about Java, Unity, or anything else, as I am about Flash.)
Also I'm mostly annoyed by the obvious hippocracy that it shows on the part of apple. (Which again, really shouldn't surprise me by now, but meh.) Because as countless people have already pointed out, it basically outlaws a very large percentage of stuff that is already in the app store. No one REALLY expects apple to come down too hard on the non-flash things here. They are basically just issuing a law that makes it so EVERYONE who uses any kind of middleware is illegal, so they can pick and choose their enforcement to suit their whims. The app store approval process already has a wide reputation for capriousness. They already pick and choose apps to ban inconsistently, frequently refuse to provide reasons, and refuse to provide any real recourse, or point of contact. This is only going to make this problem worse.
So yeah. I don't get mad at apple because I feel I have some "right" to use flash in particular. But I do feel that I have a "right" to develop using whatever tools I see fit, whether they be Adobe's products, or blond-haired employees, and that apple should get out of my business, and only concern themselves with my product.