Certegy isn't checking bank balances when you are punched into the register. It's checking your drivers license number and checking account number to see if you are on a blacklist. This list is composed of anyone who has a bounced a check with any check verification company (they all work together) and a few other bad debt situations like abandoned bank accounts with negative balances. So if you arrived in a limo with President Obama and he stood up giving a thumbs up while you presented a $2.00 government check with your drivers license, the check would be declined even though the account has billions of dollars in it. These companies also flag customers for excessively large checks and multiple checks written in a short period of time. These aren't declined but are required to be called in on a telephone for approval. During this process, the name on the license is matched to the check and your bank is called for for an actual available funds inquiry.
It's easy to blame a store, but understand this... Checks are like IOU's and stores have received millions of dollars of worthless ones. Certegy charges stores a small percentage of the amount of each check written to back those checks. In other words, if a Certegy approved check bounces, they pay the store and become the new owners of the worthless paper and try to collect on it themselves. Having said this, the rules of the game are that the store can only accept checks approved by Certegy and it must be electronically approved or a manual valid approval code entered. In other words, if Certegy declines your check, the store has no possible way to complete the transaction on the register. There is no "trust me" or "take my word for it" or "I have a billion dollars in the bank" bypass for you.
Here's a tip for ya... If you have all that money in the bank, just whip out your ATM card, swipe it and be on your way. I'm sure the customers in line behind you would appreciate it as well. You'll have your stuff, the store will have it's money and everyone will be happy except Certegy whom won't make a nickel on the deal!