When you move a bone, all child bones, are moved to. So it looks like you are stretching the whole thing, when you adjust every bone's z-offset.

So... if you have e.g. three bones in a vertical chain and they are named A,B,C, A is the highest one, you move ONLY C to move all bones ABC on the Z Axis. If you move then B on the X Axis for instance, C remains, but A is moved accordingly on the X Axis.

I hope that helps and you got an image on how it works.

cheers
Christian