Only the super user can edit the default output of a Page Type

Permalink
I'm trying to do the following:

1. Go to "Dashboard" -> "Pages & Themes" -> "Page Types"
2. Go to the "Output" button against any Page Type
3. Click one of the Page Template "Edit Defaults" button

Then when I'm on the default page, I can see an "Edit Mode" button. But only the Super Admin can see it, and I can't find any permission settings to grant this permission to any other type of user.

Concrete version is 5.7.5.13.