It depends on who you mean by "they". The salesmen are usually paid a percentage of gross over invoice. So if they sell at invoice, the salesman doesn't get paid any extra for the sale (although he still makes minimum wage for the time he spends on duty.)
But the dealer receives two invoices, one with holdback and one without holdback. Almost always when they discuss invoice price, they are talking about the invoice with holdback. Ford "holds back" a percentage of the total cost of the vehicle to cover several different future expenses. The big future cost is floor plan (interest). The holdback is enough to cover a few months of floorplan costs for that vehicle, plus a bit more to cover warranty chargebacks, parts purchases from Ford, and such.
(A warranty chargeback is when a dealer tries to get Ford to pay for a fix that is not covered by warranty. When Ford determines the Dealer was playing fast and loose with the rules, they "charge back" the dealer for the cost of the denied warranty claim and it comes out of the hold back funds.)
So the dealer pays Ford the invoice cost including holdback up front, but periodically Ford and the dealer "settle up" the hold back account. If there's any money left in the holdback account, Ford writes the dealer a check for that amount. But often that account is "in the red" so the dealer writes Ford a check.
The holdback account is a cause for vast misunderstanding between customer and dealer. Customers who have heard about something called dealer holdback assume the dealer gets all of it, and therefore makes lots of money even if he sells the vehicle at invoice or below. Dealership management knows that the holdback account is certainly not "profit", but pays some of the expenses of the dealership.
When so-called advisers tell you to get into the dealer's hold-back funds, they often don't have a clue as to whether there's any money in the holdback account. Usually the dealer receives very little back from the holdback account, but a dealer that manages his inventory well and doesn't try to cheat on warranty claims can get some back. It's an accounting nightmare, so unless you have at least a bachelors in accounting, don't try to figure it all out. Just understand that invoice price is an excellent price, and if you can buy the vehicle at invoice (minus rebates) then you done good.
But there are lots of stories about that truck that only a mother could love sitting on the lot, and it's been sitting there for months and months. And the dealer was glad to let you negotiate him down to a bunch of dollers below invoice. Yes that happens. But that unsold truck is never the one I want, so I never get that super-good deal.
