It seems to me the real issue is whether one speaks of careers or employers. Take me, for example. In addition to college teaching I have held four distinct non-teaching jobs since earning my baccalaureate degree. On the other hand, if you count every employer for whom I've done college teaching, there have been 10 of those, part- and full-time.
Have I had 14 careers or only five? I believe Bialik's column confuses these two issues. I think of myself as having spent most of my life in one career - college teaching - and most of that time for one university. Go see his column and make up your own mind.