Jeff,
I'm not sure why that's happening. It's definitely strange, and not an issue we've ever heard of. Unfortunately, we can't set up the application for you, but if you can access the application area with your own Facebook account, you should be able to get over this obstacle.
First, you'll need to create the application with your Facebook account. Once created, there's a "Roles" manager where you should be able to add your clients Facebook account as an administrator. From there, things should work just like normal.
If you can't add the other Facebook account, or you don't want to create the application initially in your name, you'll need to contact Facebook to understand what is wrong with that account. It could be a bug, or the account is for some reason blocked from creating applications due to past behavior. I haven't heard of this latter problem, but Facebook does what Facebook does
Hope that helps get you started,
Alex