i have worked at new card dealers for over 30 years. i spent a few years in the used car area during this time. i have also been part owner of a used car lot.

fist EVERY STATES LAWS ARE DIFFERENT. so what happens in my state might be different than yours.

first EVERY USED CAR sold is sold AS IS by a dealership. even new car demos are sold as is. there are factory warranties and other extended warranties sold by the dealer. but the cars are sold as is. for the most part once you sign the papers and pay the $$$ you own it.
there are certain laws regarding the window inspection sticker they have to follow. basically if it's checked off on the window sticker as being good it HAS to be GOOD. if it says the radio works the radio MUST WORK. it doesn't have to work perfect, but if it works they are good to go. the most serious violation is emissions systems. basically a dealer cannot sell a car that won't pass emissions.
structural damages are usually part of this window sticker. it gets to be a gray area of repaired structural damages. if you don't easily see the repaired areas the enforcement agencies usually side with the dealer. now if the car has hacked repairs where a blind man can see the damages and drives down the road sideways then the buyer has a case.

on writing on the back of the original title.
as least in Wisconsin the buyer will not get the original title when buying a car from a dealer. the buyer signs the title on purchase and then it's sent by the DEALER to the DMV for processing a title and mailed to the buyer. in the past some dealers went to the DMV and got titles for the buyer over the counter along with plates. the laws have changed a bit and there are satellite processing places but this is irrelevant to the main subject.
when a dealer buys a car from another dealer it gets signed at the first dealer then sent to the next dealer. he signs it and if it goes to another dealer the same thing happens. you can usually do this 3 times and then the dealer must get a title in their name and the process starts all over. if the title is altered in any way it becomes void and a complicated process begins to get a title.

as far as carfax not showing damages.
in most cases carfax is mostly a marketing gimmick. if repairs are not done at a licensed repair shop at RETAIL it usually won't show up on a carfax. i own a 08 bullitt mustang. the car has been totaled 3 times, one of those times it had significant structural damages. it was repaired off the books and the car has a perfectly clean carfax. if the hack rocker repairs were done internally it usually won't show up on a carfax. also there can be significant delays between the actual repairs and when it shows up on the carfax. at the dealer i work at now has purchased back cars 7-8 months after the sale because of a surprise report of structural repairs done in the past. they didn't HAVE to do this, but we have been in business over 100 years and their reputation is more important than a couple of thousand $$.

hope this info helps. but again EVERY STATE HAS DIFFERENT LAWS. if there is a major problem with the car contact a lawyer in your state for accurate info.