The host component for the "PopUpMediaBrowserSkin.mxml" is "PopUpMediaBrowser". So for any changes in PopUpMediaBrowserSkin.mxml to get reflected in the application, you would need to override the existing skin.
For that, perform the following steps,
1) Place the modified skin file in any project source folder ( for ex: com.esri.customSkins folder)
2) open the default.css file (default package) and include the following namespace,
@namespace skinComps "com.esri.ags.skins.supportClasses.*";
3) Also inlcude the following skinClass reference for "PopUpMediaBrowser",
skinComps|PopUpMediaBrowser
{
skinClass: ClassReference("com.esri.customSkins.PopUpMediaBrowserSkin");
}
Regards,
Rama