Airbags deploy at an equivalent of hitting a wall going about 15 mph. They probably want to make sure everything is fine before paying for it. I used to work in auto loss mitigation and a lot of people who end up having issues with their cars, not enough to qualify for a lemon law, end up defaulting because the repair costs are too much or they feel they shouldn't have to pay for a car that they believe is a lemon or had hidden damage. Your credit union us probably trying to avoid that type of scenario.
Are you certain you still want this car with the new info regarding a major accident? The lender may be doing you a favor. Maybe a different car would be better for you. Did you have a PPI?
Very few lenders will approve loans for private party purchases and 3rd party used dealerships because of repaired salvage titled cars.
V6 Mustangs especially are ubiquitous: IE you should be able to find another one the same color, same options quite easily. If it has to be used consider CPO (Certified Pre Owned).
CarMax and TrueCar will have them as well.
The process will be much smoother and neither car you are 1099. I am 1099 and recently out of bankrupcy was approved by CarMax.