Right issue with REST API on subwiki in path-based multiwiki

To reproduce :

With a non-admin user, open a page in a subwiki of a path-based multiwiki, and in the javascript console run the following :

new Ajax.Request(new XWiki.Document("WebHome", "Sandbox").getURL(), {method: "GET"});

And then compare with the equivalent REST URL :

new Ajax.Request(new XWiki.Document("WebHome", "Sandbox").getRestURL(), {method: "GET"});

The second one answers 401 unauthorized.

The unauthorized status is returned in XWikiResource.java, around line 205 :
throw new WebApplicationException(Status.UNAUTHORIZED);, after no document is returned by the XWiki API.