At one point in my life I sold cars and from what I saw, three things stick out.
Unless the other dealership was in the same network, eg ABC Ford of City A, and ABC Ford of City B, they never had possession of that truck. So, no REAL application for a loan could be sent in to a bank, just a letter of intent, if one was sent at all.
With a letter of intent, a soft pull is done, most likely by the dealership, where they then attached that score to the LOI that the bank has an automated program send back an automatic decline, an officer review reply, or a tentative approval (eg tier 0,1,2...8).
The tentative approval is just that, Tentative. Sometime after a lender has a loan officer look at the full application, something prompts them to change their offer. They have internal guidelines, but lets say an app is right at the line for 2-3 of the things they look at, they chose to lower the credit tier or decline the app.
The dealership then goes back and looks at what other offers they had. Let's say they had a Chase offer at 3.25% and a CapOne for 5.25% they would say you're approved at 3.5%, they make their money on the .25%. But after Chase looks into the app and sees that, let's say you have been on the job for actually 11 months and not 1 year, and you said you made $50,000, but your 1040 shows $48,200, and you have moved 6 times in the last 5 years. They comeback and say no he is not a tier 2 but a tier 3 @ 5.5%. They switch to CapOne and say your rate has in fact gone up to 5.5%. Ultimately you never had a loan to start with - only a letter of intent. The other thing could be that the dealership finance manager looked at your credit score and guessed they would offer 3.5%, when they sent in the LOI it came back higher than he thought. Or he was BSing you, so if you price shopped while they looked for a truck you wouldn't get far.
They didn't find that Truck, or it was not what they thought it would be. If a dealership sees a truck in inventory at another dealer they call and ask if it's available, if they have it, and it's not being used as a demo for a sales manager, they agree to send them something else for the trade, a car, or truck or whatever. A transfer driver of some sort hops in that trade, drives the 30 minutes - 6 hours away and comes back so you can sign the Real Application, TODAY! while you're excited about your new truck and willing to do whatever you need to do to get it. Because they said it would take 2-5 days to "Ship" it tells me it wasn't available. Time Kills Deals, and dealerships know this: they want to sign you TODAY! Some dealerships want "honest" money or a deposit to go get the truck, but reality is that that is a trick to test you to make sure you are going to follow through after they spend the gas and add mileage to a car. But if it takes 2 days+, The truck isn't out there, or the dealer doesn't have a vehicle the other dealership wants back, or no other dealership likes dealing with them. The only way it would take that long is if you were looking for something very rare, an odd color in an unusual configuration. Like a top end model in a low selling color, or configuration you had to have that wouldn't sell well - like you wanted all the options on a car except a cigarette lighter, you get the idea. 99.99% of the time a good enough truck is available.
Deposits are BS. They don't setup any kind of real contract, notice most of the time they want a check. Because holding on to a check is about as binding as making you wear a chicken suit to get a rebate. All it is, is a test to see if you will go through with signing the deal. As an example of why you don't let time pass on a car deal is shown in this. One time we had a couple want us to find a Cadillac Escalade Hybrid in red with every available option. Total cost was about $85-90k. Only two new Red Escalade hybrids were for sale in the country at the time, one was in New York, and the other was in San Fransisco, and our dealership is in Texas, and neither was wanting to trade with us, so we ended up having to buy the SUV from one of the other dealerships inventory. That is a very rare thing to do by the way. We took a 25% down payment, around $20,000, in a check. We flew a driver to wherever the SUV was and then drove it back to Texas about 4 days later. The couple came back and hated the color, they would not take the SUV. The General Manager was pissed, he spent around $1000 just to bring the thing to Texas, not to mention he had to buy the thing. The couple walked and there was nothing the sales manager, GM, or salesman could do. We had not been able to deliver the car, and ultimately the dealership ate the loss, but it shows that deposits are useless. You can't sell something you don't own, and dealerships know it.
Long story short, you can't claim a damage you never experienced. Not having something happen that you wanted to have happen is not a damage because you can't show a real economic loss.
One other thing, When you sign the paperwork that you thought was an application, it was an authorization for them to pull your credit and the fine print at the bottom is boiler plate defense against getting sued for everything imaginable. Ours took up about half of one page and all of the back of the second page.
I know dealing with car dealerships is hard, working at them is just as hard, and I'm sorry that you had to deal with it, however the simplest and smoothest car deals are the ones where you pay full price.