Transfer case

Hello, so my car has been making this crackling noise for about a week or two and eventually it started jerking drastically. I had it towed to the dealership and they told me that my transfer case was cracked. They stated that my car has three different tire brands (which is all the same size) but the tread on them are different which caused the transfer case to crack. They told me that I would have to purchase 4 brand new tires from them which would total $800 before they can change the transfer case which is covered under warranty. They also stated that once that is done then they can look to see what else could possibly be wrong with my vehicle. Is this accurate? Can the difference of the tread in my tires cause the transfer case to crack?