Earlier quoted context omitted.
As a Technical PM, I fought against a former boss when they wanted to forego native controls because they wanted their app to be branded, because without a custom look they felt that their app would not be unique and memorable. If an app can't survive on its usefulness alone, it probably shouldn't exist. As a user, if an app doesn't have a native UI, I disregard it unless I need it for a specific and mandatory use.
I believe Winamp became so popular because it had such a unique UI, that was also incredibly customizable. Compare that to Windows media player at the time... On the flip side I want me email client, my desktop authoring tools and admin tools to all look and act the same.
Now that screen resolutions vary quite a bit I suppose it wouldn't work as well as when all monitors were mediocre 800x600 or glorious high res 1024x768. Ah, the nostalgia.