I understand all that but I'm afraid I'm still not wholly satisfied.
You don't need to be satisfied. You only need to comply.
If the iPad is certified as an EFB why can I not use my iPad on the same aircraft that is using an iPad based EFB?
The Ipad is certified for that specific operator, by serial number, in the cockpit, using specific functions only, with a specific power supply, as the result of research, demonstration, and the approval process. YOUR Ipad does not have that approval.
Are you planning on going to the trouble and expense of putting your Ipad on the certificate holder's program, and then using it only in the cockpit for charts? You might stand a chance. Otherwise, turn it off, do as you're instructed, and you won't have any problems.