Welllll...I once stuck a 308 round in a 270 win rifle--
Back in the early sixties, while stationed at an air base in Oscoda, Michigan, I rented a Model 94 Winchester from the recreation department (the rental fee was a dollar a day) to go on a bear hunt in the Upper Peninsula in some cedar swamps near Whitefish Point, with three Airman buddies.
Though the four of us never saw a bear (plenty of blueberries though) and never fired a shot, when it came to returning the rifle I couldn't get the round out of the chamber (or maybe from the magazine because I'm not sure if it's even possible to shoehorn a .308 round inside the chamber of a .30-30; I can't remember which). The personnel from the department was able to extract a .308 cartridge from the Model 94, chambered in .30-30, and gave me a well-deserved scolding.
Apparently, I had left a .308 cartridge in the pocket of a hunting jacket that I had wore in a previous deer hunt and managed to get it mixed with the .30-30 rounds. My guess is very bad things would have happened if I was unlucky enough to have fired a .308 cartridge from that Model 94 (again, if that's even possible). Being lucky trumped being dumb that time.