I'm a large tech company employee, and I use "Not my job" sometimes because it means that I believe that the issue could be handled more effectively by someone else, or that I should not be the one to address the issue for political reasons. So it's less of a "not my job" and leave it at that, but more like "not my job, but Jane over on that other team is closer to that code and has a better understanding of what's going on."
I was speaking more of different departments giving the run around pointing to each other in a circle and saying "not my job". The problem I see here as that there are many things that need to be done and rarely is the coverage of "job descriptions" 100%.
