"For this site" not available in content reference properties

Description

Steps to reproduce:
1. Go to admin -> Manage websites and enable site-specific assets for your site.
2. Add the following code to any page type:

        [AllowedTypes(typeof(GenericMedia), typeof(ImageFile))]
        [Display(GroupName = SystemTabNames.Content, Order = 20)]
        public virtual IList<ContentReference> ListOfThings { get; set; }
 
        [AllowedTypes(typeof(GenericMedia), typeof(ImageFile))]
        [Display(GroupName = SystemTabNames.Content, Order = 22)]
        public virtual ContentReference JustOneThing { get; set; }

3. Edit a page of the page type used in the step above.
4. Edit either of the two new properties.

Expected:
An option to select images from the "For this site" folder.

Actual:
No "For this site" folder available.