Trust us

"Just leave your credit card number with us and we'll let you know when the charge goes through," said the tire store guy.
"It'll be fine."
I was a touch apprehensive because first of all, I never know if I can trust a car repair garage and secondly, their computers hadn't been responsive all morning.
I had taken my car in for squeaky brakes.
Having just paid $300 for new brakes on our SUV, I was not anxious to pay for more for our second car.
So I was relieved when the technician came back and said my brakes were OK but I had "brake dust" building up and needed it all cleaned off.
"Brake dust?"
I'd never heard of it but if the guy was a crook, he would've just sold me some new, expensive brakes, right?
I reluctantly agreed to have the dust dusted and have some fluids changed out. In exchange, I would get a "free" oil change and they would check my alignment.
About $200 and a couple of hours later, I was trying to pay my bill.
The machine refused to take my card.
"Man!" said the tire guy. "The credit card machine isn't working again!" he yelled to the others in the shop.
He tinkered with the device and searched around for some help.
The machine refused to stay on long enough to run the charge even though I swiped and swiped.
Finally I offered to go home and get a check.
"Could you?" he asked hopefully.
"Could you pay with a check?"
I explained that I would have to run home since I never carry my checkbook with me anymore.
His colleague came up and said, "Just have her leave her credit card number and we'll run it when the computers come up."
I gulped. Oh. Ok. What assurance did I have that I wouldn't end up paying thousands of dollars in charges or, at the very least, the same $200 bill several times?
"We won't do anything like that," the guy promised. "Trust us."
Why not?