That's the reason. If you rosin in both directions, the cake will adhere to the hair when you stop to change direction, and will generally result in a broken hair or two (or few).
Obviously, this is more of a problem with soft rosins, and less of one with hard varieties.
If you were to let the cake go off the end of the bow before reversing direction, i.e. never stop the bow on the cake, there won't be any issue.
Thanks for the response. This is the first explanation that I have heard that makes any sense to me. I was just about to chalk this up to "just another double bass urban myth".
I don't rosin all in one direction, because it never seemed to work very well for me. I use the scruncha-scruncha-scruncha method, from frog to tip, short strokes. It works a lot better for me (better distribution of rosin throughout the bow, no missed spots). So far, I'm not aware of any damage to the hair.
I was taught the frog-to-tip-only method and have looked scornfully at other bassists going both ways. However, I was just looking through Portnoi's (former BSO principal) method book which was mentioned on another post. He recommended rosin be applied in both directions. What do I know?
However, I was just looking through Portnoi's (former BSO principal) method book which was mentioned on another post. He recommended rosin be applied in both directions. What do I know? 
