This is second hand information as I am not a millionaire, but I work with such people everyday and have an understanding of how they handle cash:
The wealthy people don't.
Definitely not if they don't have to.
Cash is a tool to them that they use only if they get benefit of it being a cash transaction (one of my friends is a re-seller and he gets a 10% discount from suppliers for settling lines using cash).
Everything else they place on a line of credit.
For people who "dislike" credit cards and pay using ATM or debit cards might actually have a very poor understanding of leverage. I assure you, the wealthy people have a very good understanding of it!
Frankly, wealthy people pay less for everything, but they deserve it because of the extreme amount of leverage they have built for themselves.
Their APRs are low, their credit limits are insanely high, they have longer billing periods and they get spoiled by credit card vendors all the time.
For example, when you buy your groceries at Walmart, you pay at least a 4% markup because that's the standardized cost of processing credit cards.
Even if you paid in cash!
A wealthy person uses his credit card to pay for the same but earns the same percentage amount in cash back, points and what not.
I am sure littleadv placed the car purchase on his credit card for similar reasons!
The even more wealthy have their groceries shipped to their houses and if they pay cash I won't be surprised if they actually end up paying much less for fresh (organic) vegetables than what equivalent produce at Walmart would get them!
I apologize for not being able to provide citations for these points I make as they are personal observations.