Is this normal? Financing used vehicle

I am in the process of purchasing a slightly used car ($37500 + tax = $41500)

My credit score is 810. The dealership says that in order to get a loan, I’d have to put $9000 down to get a rate of 7.85%. They told me that since I have “no credit history” that’s why the rate is high. I always pay my credit cards off in full every month and only have one card I use to frequently. Prior to this I had a different card that I also always paid off in full dating back 20 years ago. That card doesn’t show up (never closed it out) and neither do any of my car leases from 15-20 years ago.

Are they just making shit up or is this actually a thing where a bank won’t give you a loan unless you have multiple cards open?