What's even more ridiculous is that for Firefox, if you change the "User Agent" it works perfectly fine.
On your hardware, using your OS version, on the single internet connection you tried, in your language, with your set of installed plugins, using your particular browser settings, and trying the limited set of features that you used to test it.
That's practically the definition of "it works on my machine."
I imagine the Skype team have a somewhat more rigorous testing methodology.