I think we are talking about different things. I am talking that when your credit card company generates statement for charges during the statement period you can (at least in US) setup an option in the card management page to pay either minimum amount or full amount of the statement. Payment is done from your checking (current) account. In States (contrary to other places) you can not push full/partial amount of statement automatically from your checking account to your credit card account - it has to be done manually, while credit card company can pull the pre-defined amount from checking account.

I really can't imagine that Chase will pull wrong amount from Wells Fargo and it will take me several month to fight it back. Last 15 years I've been using this setup, there are millions like me and I do not remember any news that credit card company pulled wrong amount from the checking account.

If you are talking about not to give third party your checking account number to pull funds from it, I'd totally agree with you. But if you want to be totally protected you should not use checks anywhere as well.

However all those efforts might be moot because if people know your checking account information and ABA number they will pull money even w/o any electronic communication. Three years ago someone printed checks with my wife's checking account number and bought >$300 stuff at LA's Walmart (we've been living in another part of the country) and paid Cox Comm's cable bills. Bank called my wife the same day checks hit the account and asked for clarification. Everything was returned back to the account next day.