I know this is an old thread, but I thought I would share my experience incase it helps anyone.
I had a problem with my oil pump, same as above. After stripping it, I figured it was missing a ball bearing to act as a valve. The oil enters the pump through the gauze. The manual pump draws it on the return stroke, then should push it up the hole that the pic above has a bearing in. I left that clear and I popped a 3.5mm ss steel bearing in the larger hole this side of the gauze.Whilst I was at it, I replaced the smaller ball at the top of the piston valve with a neww ss 2.5mm. Now works as good as new!!
The model is a Mac 4000. 16" bar. Can't fing any info on it anywhere!