what is the problem with discount and some of these tire joints these days.

Uhhh, the 'burn up' due to changing one tire on an AWD vehicle refers to the transfercase/ transmission going out which DOES happen, whether or not your salesperson/tech/whatever was smart enough or experienced enough to speak correctly when getting pressured by a lawyer or an angry husband type doesn't matter; changing ONE tire on an AWD car (or not regularly maintaining/rotating tires) can and will result in premature wear (chevrolet has a TSB that states it takes 1/16" difference in diameter to cause premature wear) of your drivetrain. I have personally changed out transmissions on a few different make AWD cars/SUVs due to mismatched tires (one had 3 different make tires in use) I also have talked to techs at Jasper transmissions (the shop I worked at used them for a while) and they agreed with the narrative the OEMs use too.

Read some of this unscrupulous lying BS
Do You Need to Replace All 4 Tires on Your AWD Vehicle? - Les Schwab Tire Centers explains a little bit more

So it could damage the transfercase/transmission. But will it "burn" the car? Or the computer? As this guy told him? I don't care what kinda pressure he is under. If you tell someone their car will "burn up" without properly explaining why? You're an idiot. He said specifically that the computer would burn up. Not any of the drive train. He was trying to scare her. Period.

Not only that, you can't tell me that every time a person with a 4wd/awd gets a flat, they have to change all 4? C'mon now. I was born at night but not last night. If that was true, no one would buy them. Who wants to buy a car that you have to get 4 new tires when you get a flat. Especially a vehicle that is aimed at rougher/off road driving? Can it make a difference if the other tires are very worn/near end of life? Sure. I can see that. Can it make a difference on tires with only a few thousand miles? Doubt it.