On the other hand, if Mozilla/Opera/Chrome used third party decoder, that would be support nightmare ("It works on my computer, but not on friend's! Please fix it!").
I don't understand the significance. The same APIs are accessible to any other browser. If someone has evidence that Mozilla, et al. have been technically locked out of using the media APIs on Windows or Mac OS X, I'd be interested in the details, and if someone has evidence that they've been locked out of using the media APIs on Linux, I'll eat my hat.
they use their vendor's decoder and nothing else
I'm not sure what you mean. If you mean something like "Windows will only support h.264 and you can't use anything else", then that is exactly wrong.
Microsoft can always rely, that IE9 will supports whatever formats they want it to support. They know, that it will play H.264, because they ship H.264 with Vista and 7 and IE9 supports only Vista and 7.
Apple can also always rely, that Safari will display formats they want it to display. They know, that Safari will play H.264, because Quicktime ships with H.264 and Quicktime is bundled with OSX, or with Safari for Windows.
If Mozilla/Google/Opera outsource this to OS, they lose control. They will not know, what the browser will display (imagine handing off control about HTML/CSS/JS to Microsoft, when IE6 was going down and Firefox up. It would be like Firefox using IE HTML control to display HTML).
Another problem from the control perspective is inconsistent support among platforms. Platform A, it will play formats X and Y. On platform B, formats Y and Z. On C, X a Z. Do you see problem here?
That is not the case for browser vendor without their OS. They cannot achieve the same effect.