I think probably there are a few missing words in the documentation?
For me the way I would think of it is, just as it says, "administrative access" allows the user to be able to edit custom forms. But not any custom forms. Just the ones "in their group". And for me, what "in their group" means, is giving the group manage access to the form.
So just like a lot of other things in Workfront, access is a two-part solution, involving visibility and permissioning. Just as you would "share" a project with any user with a plan license, but then set their sharing to Manage if you want them to edit it, so too would you "share" a custom form with any user with a group admin access level, and then additionally set their sharing to Manage if you want them to edit it.