I wonder what else may have been damaged putting a lug nut on that tight? Wheel stud, wheel, brake rotor?
I've had to deal with over-torqued lugnuts a lot at the race track. First-time racing mechanics can get a little over-zealous when reinstalling wheels...
Over-tightening a little generally won't hurt anything. Over-tightening a lot can.
The torque spec for any fastener is designed to apply a specific amount of stretch to the fastener to lock the threads together and prevent the assembly from loosening. The longer the stressed portion of the fastener is, or the larger the root diameter, the higher the torque value is. The application affects the specified torque as well, as does the method of assembly (type of lubricant used, if any.)
An over-torqued assembly won't damage anything UNLESS you stretch the fastener so much that it undergoes plastic deformation. That is, the fastener stretches so much that it can't return to its original length. You can check for this by running a plain nut (not a lock-nut!) the entire length of the threaded portion of the fastener. If it reaches a spot where it does not turn easily and the threads appear clean and normal, then the fastener has likely stretched and is now junk. Its yield strength is much lower than it was before it stretched.
Tire shops hire workers based on how fast they are, not on how contentious they are. They WILL use an impact to install your lug nuts. They MAY grab a torque stick, or they may not. They MAY grab the right one. They MAY know what the torque spec is for your car in order to choose the right one, but I doubt it.
Look at all the cars on the road with one or more missing lug nuts. The reason? The wheel stud has snapped off because someone stretched it.
I always assume they don't know what they're doing and re-do each lugnut when I get home. Whenever a wheel comes off, I check for stretch.
Oh, and for the race car, impact wrenches are NEVER used on the lug nuts!