I agree that they probably did **** up the tool. The factory lug wrench is for emergencies only and is cheap crap. If you damaged a lug using that crappy tool, it's not surprising. That tool is typically either stamped metal formed into a hex, or it's the even crappier "tire iron" style with horrible tolerances. Use a proper sized deep well socket and a breaker bar and you will never have issues. I have never used a factory tool on any lug nut now that I think about it. I only use the hooked/rubber coated end to pry off center caps.
Ford's lugnuts have a stainless steel outer shell to keep them from getting as rusty as normal chromed lugs get. If you beat the crap out of that thin outer shell with an impact and/or a loose fitting socket, it's going to roll over at the corners. They don't swell. The rolled corners are what makes it stick in the socket. Again, use a proper sized deep well socket and a breaker bar and you will never have issues. You can use impact tools no problem, but only if you have a tight fitting deep well socket on the lugnut. If the offical size of the lug is 21mm, but a 13/16 socket actually fits tight with no slop- using the 21mm will destroy the lugs. You have to get a socket that fits tight with no slop, and never use the "well this is close and it will remove them so it's good enough" size. If you do that one time, the tight fitting socket will never fit again and it just gets worse and worse as you used oversized sockets to accommodate the previous damage.
I agree with most of what you say, but in my case the outer portion absolutely did swell. If that's not the best word to use, then they became "loose" on the main nut underneath. Some would move back and forth on the main part of the nut. This after a few tire rotations where the tire store used an impact to remove the nuts. I became aware when I tried to remove a flat tire and i had to drive the socket on with a hammer. On one lug it actually tore the outer cover. What a hassle. Replace the factory lugs and be done with it.