Can a car dealer "take" a new car back after 3 weeks if financing doesn't to through?

My daughter's 19-year-old boyfriend was ecstatic when he learned he would be able to purchase a brand-new car without his parents as co-signers. He bought the car on Oct. 13 and has been driving it happily since. Within the last several days, the dealership has been calling him at his house to tell him that he needs a co-signer or else they'll have to "take" the car back because the gentleman who approved his loan apparently didn't do something correctly and has since been fired. And apparently his loan wasn't approved. My question is, can they do this? He has limited - but good - credit, and has been working at his job for about 15 months, in addition to going to college part-time. And if they CAN take the car back after this time, do they have any right to request money from him for the time he's had the car? He really doesn't want to give the car up, and it seems that since they made the "mistake" of granting him a loan without co-signers, it's not his problem. Should he keep the car and take the dealership to court? Does he even have a case? And shouldn't the dealership have verified that a 19-year-old young man was qualified before allowing him to enter into an agreement and drive the car off the lot? He's trying to establish credit on his own without his parents (who, sadly, do not have good credit), and no, we're not willing to be co-signers for our daughter's boyfriend and put our own very good credit rating at risk. :-) Any advice would be greatly appreciated.