My parents are like this, too!
My dad's very proud that he's never had to take out a car loan. His first car was $500 and he drove it 8 years (yes, I have to hear about this all the time lol) and ever since he's always saved up for his cars.
He has started collecting frequent flier miles, though, so he uses a card. Otherwise, he'd pay for everything in crumpled dollar bills if he could!
We're lucky, though, to have good examples from our parents. I'm sure in like forty years we'll be lecturing our daughters for charging a Diet Coke, too!