NewDocSet.aspx - Access denied when calling from permission interrupted sub website

I have researched something further:

I have a WebSiteCollection and a SubWebSite. In the root site I create a content type based on document sets. Inside the SubWebSite I add this content type to the default document lib. The permission inheritance from root to sub site is interrupted.

Now I give contribute access to a test user to the document lib only. No acces to root, no acces to sub, only document lib access. When the user calls the link directly to the doccument lib, he can see the documents. When he now wants to create a document set, he gets the access denied to the _layouts... NewDocSet.aspx site. When I now add the test user to a new created WebSite group with minimum rights (Display only), than the user gets the possibility to access the NewDocSet.aspx page and he could create a document set. But he could also see the web site content and see the other libs and list. I don't want this, so for every libs and list I break the WebSite permission inheritance and remove the newly generated group containing the test user. Now the test user sees the other libs in the web site content page, but could not access the lists.

Not nice, but works!