The split-image rangefider on the Argus C3 is a lot more reliable and easier to use than almost any other old camera. Often, a little cleaning of the optics is all that is needed to get the rangefinder working like new.
On my cameras -- all post-war models -- the little top screw does clearly change the vertical image alignment. Just turning the bottom screw, however, accomplishes nothing. If you disassemble the rf mechanism, what you will discover is that under the larger screw there is a little slot oriented perpendicular to the long axis of the camera. To adjust horizontal alignment you need to loosen the screw and then move it toward or away from the lens.
That sounds a bit easier than it is. In fact, if you can see the screw move when you push it forward or back, you have gone way too far. Looking through the rf window, you will see that the split images cannot be brought together, so you need to gently push things roughly back in place and start over with very gentle nudges to the front or back edges of the large screw head. When you get things lined up properly, you can tighten down the screw, but that may throw the adjustment off a tiny bit. The trick seems to be to make ever-smaller adjustment movements, and to allow a little margin for the final screw tightening. Cleaning and lightly lubing the rf mechanism may make the process a little easier.
A useful target for the adjustment process is a phone pole a couple blocks away; sight on it and move the rf adjustment wheel to the infinity position, which should bring the split images into perfect vertical and horizontal alignment. Getting the focus set perfectly at the infinity position should result in proper focus at all the intermediate positions as well. Once you are satisfied no further adjustment is needed, it may be worthwhile to put a drop of paint or glue on top of the screws to insure that everything stays in place.
I can't imagine that the Argus factory technicians used the kind of hit-or-miss method I've described to get the rangefinder adjusted. My guess would be that they had some kind of jig with micrometer adjustments to get the job done. In any case, it is a task that can be accomplished even without any special tools and it is really much more a matter of persistence than of skill.