Yes, if the stud broke as the nut was being removed it would seem that the damage was done when the wheel was installed and the nut over tightened at a previous service. Used properly an air impact can be used to remove and install lug nuts with no problems. Or apparently so. Neither myself nor an employee ever broken a lug stud in many years and more than half the business was fleet work. And we were doing 100 brake jobs each month.
I’ve had two broken studs in my almost 40 years of driving…One happened while I was driving (heard this clunk as I was driving and when I stopped I noticed one of the lugs was gone)…The second time was when I was trying to remove a wheel to do a brake job “SNAP”…Both times I just took the car back to the place that last pulled the wheel and they fixed it for free…no questions asked.
Tire place I go to now Nashua Wholesale Tire they put the tires on with the air-gun just to get the lug-nuts snug…then they use a torque wrench.