Who can add users to the Term Store Administrators field in the termstoremanager.aspx

In the Term Store management tool (_layouts/15/termstoremanager.aspx) what permissions does a user need to have to be able to add/change/remove accounts and groups listed in the Term Store Administrators field.

I am guessing that they need to be Administrators of the Managed Metadata Service Application?

I ask because I have a user who is Admin of the MM Service App and is listed in the Term Store Admin field but cannot add or remove users in the Term Store Admins field in the Term Store management tool

Thanks

J