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This blog post does a good job of pointing out the shortcomings, misconceptions in the original, cited article.

Even if you don't read the post itself, this point needs to be made: using Flex and using AJAX in your web application is not an "either/or" decision. You can use both technologies in the same application (the article mentions the code libraries that exist to facilitate communication between the two technologies).

"Flex is also 100% open source. Its programming languages are based on open and standard languages such as ECMAScript and XML. "

This is deceptive nonsense.
The Flex compiler is just a tool to produce Applications that run on the flash runtime. It is correct that the tools to create a flash application are open source, but the platform these programs are running on is closed and proprietary.

"but the platform these programs are running on is closed and proprietary. "

Don't forget that the VM it runs on is also open source. Adobe donated the Javascript VM sometime last year to the Mozilla Foundation and it became the Tamarin project. I think Flash will eventually follow Java in being completely open source. I'm not sure that I would count on Flex Builder being opened up though.