Tce-setup changes it to "USER":staff, Mplayer couldn't if it didn't have a tce.installed directory in the extension. "USER" being normally tc, unless another user is specified.
The extension should be root:staff/775 for tce.installed as if tce.installed gets its attributes overwritten by the extension, "USER" may be a different user than tc. And if the perms are tc:staff/755 or root:staff/755, another user cannot write to tce.installed. Tce-setup changing the owner to "USER":staff is ok and normal.