If you have access to change the permissions, you can change the permissions, including the permissions of admins and special accounts.
An alternative that may work for you is to set up the folder to inherit permissions from a parent folder that he can't change the permissions on. Define the permissions you don't want him to be able to change up there, and propagate those permissions down. Of course, he would be able to disable inheritable permissions and remove those permissions, but there's really not a lot you can do about that... other than telling him not to, and warning him that if he does, you'll revoke his permissions-changing access, and be applying the permissions you feel are appropriate from then on.
(I've found that pretty effective - "Here's your access, don't do [blah] with it, or generally screw around with it, because if you do, I'll yank it and you will find yourself subject to my schedule, whims and general malevolence.")
EDIT: I actually had another thought for a possible solution, as I got assigned an AdminSDHolder problem. You could always write a script to check permissions on that directory tree at regular intervals (say every hour), seize ownership if necessary, and then reapply the permissions you want/need to be present in addition to what the coach wants.
Honestly seems like more trouble than it's worth to me, when it's so much easier to warn/threaten the user against dumbassery, but YMMV. And now that I think about it, this might be a solution to a problem in my environment too... so thanks for asking and bringing me to think of it.