They're unhappy that they made less selling the car than they expected to.

Not really true. Most dealer profit on new cars isn’t in markup. It’s on the financing, sales incentives, and the service dept.

If you negotiate an all-in price that's a $1000 lower than a typical customer, that's straightforwardly $1000 they don't get. The fact that your price was lower doesn't cause their other sources of revenue on the sale to go up.

If they give you a deal but get you to agree to a higher finance rate, they make more money

Agreed - you should always look at all-in costs, including financing. Normally better to get financing somewhere else ahead of time if you have good credit.

That is still misleading from the overall profit picture because the dealer can be getting points back on the loan.

That doesn't effect the price you ultimately pay, just who gets what.

(E.g. your "true" interest rate is 2.5%, the dealer gets you to take a loan at 3.9%...they pocket the 1.4%)