Did your friend's Mustang have wider or better tires than yours? If so,the added traction will increase the tilt because more of the engines' torque is being transferred to the body because it is more difficult to make wide tires spin. The same is true for tires with high traction ratings.
OK, guys, this is a different scenario of lifting the front due to excessive torque like Fast and Furious cars, but what I mentioned was the car was moving ahead doing a burnout but not in straight line and slightly tilted on one side. I had my Mustang for 2 years and know how 450 hp in 1.5 ton body do the burnout in a straight line, plus that car owner knew that issue as a known problem since he bought and couldn't rectify that deformity probably due to expensive repairs.
Yeah you are pretty much spot on, once a car breaks traction the tail end will try to overtake the front end. Fishtailing. Nothing to do with driveshafts and balances. An unbalanced drive shaft will cause nasty vibes even when driving like a nun above a certain speed.