I have actually never had a dealer pull this on me (and if one did, I would simply walk out the door), even though I always have financing already set up with my credit union before I ever start talking to a dealer about a car, so from their standpoint I'm paying cash. However, every dealer but one has tried to either sell me their financing instead, or sell me a lease deal instead of a purchase. (The one that didn't knew there was no point because I was a GM employee buying a GM car at that time so every single aspect of the transaction was already predetermined.) I've never taken them up on it, but the fact that they try so hard supports your hypothesis that they aren't making any real profit on the sale itself, but only on the financing.

(When I was working for GM, which was some time ago, I had access to enough numbers to make it clear that GM itself was not making any real profit on the sales of any vehicles except full size trucks and SUVs; all of their profit was from GMAC, the financing arm. I used to say that GM was really a financing company that happened to make vehicles on the side. I suspect the other US automakers are similar. I don't think most non-US automakers are; their incentives are different and they are mostly run by technical people, not financial people.)