Can a ball joint be broken during routine maintenance?

Went in for rotation, balance, alignment, & oil change. Pulled car out of parking lot after maintenance & noticed floating sensation, clunking noise, steering column to right at 45 degree angle from normal, yet driving straight (at times). Car veered to right with seeming loss of power intermittently. When I returned to the shop, they put it up & told me (with stunned looks on their faces) that my right lower ball joint (same side it was veering toward) had "fallen out". They showed it to me & sure enough, it was hanging out about 1 1/2 inches, lopsided. I spoke to two of my prior mechanics from another state who said they couldn't think of any way that it could be broken during maintenance, unless someone pulled the thing out & I don't think these guys are good enough actors to pull off the aforementioned expressions. Another local mechanic said it well could have been broken when the car was lifted for the tire rotation, but I think he was trying to disparage the competition?