I wrote a lot below if you'd like to read it enjoy, if not sorry for taking your valuable bytes :) I directly answered the questions up here first:
Why is this?
It's a confusing matter read below for the why details.
Perhaps they mean to say that Flex won't run "out of the box" and requires a plugin?
Or do they mean it won't run at all?
Using the flash builder tools (the bin folder in the SDK) you can compile for native desktop application, desktop web browsers, native iOS application, native Android application. Android with FlashPlayer plugin installed will show Flash content within the web browser, iOS will only run the ones compiled with AIR, not in the the web browser but as a native app.
Every time I think I've reached a definitive conclusion, some post on SlashDot or CNET directly contradicts it. So what's the scoop? Can one take an existing Flex application and run it on iOS/Android?
Yes, if using AIR and run as a native app on all three platforms (the desktop Flex API is for the most part a superset of the web Flex API), your other points about performance and form factor are valid and should be considered though. The nice thing is you can write your model/controller code in a common library in AS3 then write separate presentation layer interfaces that all share the library.
Here's the very long version:
Using the flash compiler results in "bytecode" in the form of a file with a swf extension using the swf format, you can read a ton more about that here:
http://www.adobe.com/devnet/swf.html
To interpret the file you need some sort of run-time similar to some degree to running WPF/XAML/C# within a .NET framework context (either desktop or using silverlight on the web). In the case of adobe technologies (rough equivalence):
- AS3 = C#
- MXML = XAML
- Flex = WPF+WCF (client side RPC not server side)
- Flash Player = Silverlight
- AIR (Adobe integrated runtime) = .NET
Framework Redistributable .dll(s)/.so(s) for desktop OSes
(Read this list very loosely please, I know XAML is preserved in the MSIL or whatever which is different because MXML is compiled to AS3 and only if a debug flag is set on the compiler does it include the debugging symbols, there's certainly tons of differences but I think this is an easy and correct enough model to use)
On iOS the browser does not allow for plugins in the traditional sense of netscape browser plugins or ActiveX plugins. For this reason you'll not be able to execute a plugin ie flashplayer or silverlight in the browser. Since Adobe did release a flashplayer for Android devices that does run in the browser it will work on those devices in the browser, however they have essentially thrown in the towel for supporting this long term, as they have to support the majority mobile device platform, iOS, in order to remain relevant (this was I think more a collective throwing in of the towel by Google, device manufacturers, carriers, Microsoft, all just following suit and trying to make the best business decision, WebKit and V8 or SpiderMonkey can probably do 99% of what Flash can do and better in some cases and WebKit will hopefully not splinter and will remain open source... frameworks and the browsers just need to get fleshed out and stabilized).
If the user installs AIR (or the runtime is packaged with the app) then a Flex/Flash (that is stuff coded in AS3 and/or MXML and compiled to a swf) can be transcoded/packaged to be interpreted by the run-time for that device correctly (be it iOS or Android or whatever RIM did, I don't think they have AIR for Windows Phone 7 and Win8 on ARM won't support browser plugins either). Part of the confusion is possibly from the fact that Apple denied the distribution of Apps that were "cross-compiled" which kept AIR out of the list of options for iOS for a good year, just after Adobe started announcing it was usable for that purpose (kicking Adobe while their down). Another part of the confusion probably comes from real vids of people who have 1 hacked their device or 2 were able to get open source alternatives to the flash player run-time to work on their iOS device (gnash was one I'm aware of from some occasional Linux tinkering, also possibly FAKE vids).