Why do cargo flight companies reposition their crew via passenger airlines?
Reposition is just what it sounds like, to move a crew from one place to another, generally the move occurs in a plane other than the one they are slated to fly. 

Both cargo and passenger airlines reposition crews all the time for various reasons. Some but not all reasons are: 


Crews are not always required to live in the place they are based. Some crew members may chose to live elsewhere and can generally fly their carrier for free to get to their starting point of the day. Cargo airlines may have deals with passenger airlines to allow this flexibility for their crews as well. 
A crew trained on a given airframe may be needed to fly a different plane than the one they just operated. 
Commercial crews have duty time limits and at the end of a "shift" they may need to get home if the cargo airline does not keep them wherever they are. On the same note a crew may be needed elsewhere to start a flight. 


A cargo airline may not fly as many back-and-fourth routes as a passenger airline so they may utilize airline flights to fill the movement needs of their crew. It is worth mentioning that some cargo aircraft do have limited seating that can be used to re-position a crew.

This cargo pilot describes it quite nicely in her blog:


  Or you expect to operate a flight, but it is changed to a positioning
  flight. A positioning flight is a flight you do for the company as a
  passenger, to get you to a certain destination from where you will
  operate, either straight away or after a layover, or sometimes you
  position after a duty. Positioning flights can be with the company, or
  booked with another airline. You might anticipate returning home on
  Tuesday, but when your block of working days finishes Friday, big
  chance you will get some more flights and will not return earlier than
  Friday. Due to these roster changes, you also might end up in a
  completely different part of the world. So in my suitcase I pack all
  kind of electric adapters, and even if I go to a subtropical
  destination, I still pack jeans and a jacket. I learned this the hard
  way by ending up in Alaska, while having packed for my trip to high
  summer Colombo.




Note: If commercial planes stop flying a fair bit of cargo stops moving any way.