It's not uncommon for a dealer to want to renegotiate even if you
offer to pay cash. There's profit in financing.

But I think HeyBub's point was that a dealer knows that the odds of
someone returning with a check in that kind of scenario are not high.
Better to sell the car for $11,400 on the spot rather than risk not
selling it at all.

Yep!

It's just a case of "working the numbers." Folks using "plastic" spend
more because they don't have to worry about how much cash they have in
pocket or even the bank.

From the view of a small businessman, the advantage of "cash" is that you
can take it "under the table" and not pay taxes on it.

"Off the books" income is worth 20% (more or less) than "on the books"
income. That's a much larger margin than the 2% (plus, sometimes, $.50)
the credit card company might charge.