As far as I know, my credit union makes auto loans based on its actual assets, i.e. it loans its own money.
About ten years ago I needed to buy a minivan for work, and decided to buy new in order to avoid the repair hassles of the used vehicles I'd had until that point. I did the price/configuration workup for the vehicle based on specific practical needs, and then determined what I could safely afford to pay each month on the loan, and from this was able to extrapolate what I would need in terms of a downpayment (which turned out to be about 35% of the cost of the vehicle). After saving up the downpayment, I applied for the loan.
The loan was accepted on the basis that even though my credit rating was typically crappy, my downpayment constituted sufficient equity in the vehicle as would assure a good incentive for repayment. I paid off the loan with no problems, I still have the vehicle, and all's well. I'll be hanging on to this one until there is appropriate new technology available for a replacement, which I'm estimating will be perhaps three more years. (Or since we expect to be living in the woods at that point, keep this minivan for cases where we need to haul cargo, and get some kind of electric or hybrid microcar for routine daily transport.)
The point of this being that the credit union apparently did things the oldschool way because it was their (technically their members') assets on the line for loans. It may also be the case that credit unions in general work this way. And if this is the case, then shifting your savings to a credit union may be a very safe move.




