When using a skin from another wiki templates override are not taken into account

To reproduce:

• in wiki1
  • go to XWiki.DefaultSkin page
  • edit it
  • put something in the Header entry
  • you can see you changed the header
• in wiki2
  • go to Presentation section of the wiki admin UI
  • set Skin entry to wiki1:XWiki.DefaultSkin

-> the header is not what you indicated on wiki1:XWiki.DefaultSkin