What is AT&T's "credit check" process during account reinstatement?

I have recently had my account canceled and I am trying to reinstate my service agreement, however, I have a few concerns:

I keep hearing that there will be a necessary credit check." 

I am told that part of it is to look and see if there was a deposit made on a phone associated with an account and that none of the credit bureaus are involved, but nothing else was outlined. So what is the process of determining wether or not and, if so, how much of a deposit will be required to continue service and why is it so elusive? I hear it is upwards of $700 and, quite frankly paying such a high amount is my last choice in the matter of saving the life of my contract, BUT allowing my contract to stay cancelled is a close second. I dont want to walk away from my contract, if I can save it, but I have to be realistic to my budget (and if I can pay the ETFs AND find business elsewhere for less than reinstating a contract AT&T decided to cancel, well….) 

My question -----> Could someone please clarify (in detail) what goes on during this "credit check" process? So I can weigh my options and protect myself.

And just for fun, if no credit bureaus are involved, why does AT&T chose the wording "credit check" when 99% of people would assume the exact same thing about what that means?