Dealership pretending to trade in a car as a “courtesy”

I’m thoroughly confused. My parents are in MN and are buying a new Subaru. The guy asked them about their 2014 Subaru that the dealership sold them 10 years ago and they mentioned they were selling it to me (I’m in CT and we’re doing a private sale for about $7k). The car is paid off, etc.

Salesman says if I send them my license and proof of insurance, they’ll “run it through” and my parents will pay sales tax on whatever their new car is (like $40k) but minus $7k.

I told my mom none of this makes any sense, and what does the dealership get out of it? “Oh you know just a courtesy, Minnesota nice and all that…” but something smells fishy to me. I don’t get what the dealership gets out of it and how they can pretend to do a trade-in?? Anyone heard of this before?