The aperture ring is a red herring here. The normal state when looking through the viewfinder is wide open — the aperture is only stopped down to the selected setting at the time of the exposure, via a mechanical coupling. The normally-open view gives less depth of field and therefore better shows the plane of focus, making it easier to focus correctly — at least in theory.

The problem is the viewfinder screen. On modern DSLRs (and recent SLRs, for that matter), the screen is designed to be as bright as possible at the expense of focus precision. Usually, you can't really accurately judge focus at f/4 or below, as you observed. So, you have to trust the AF system, which can often indicate focus even in manual-focus mode.

(A DOF preview feature, by the way, works by activating and holding the aperture stop-down coupling without tripping the shutter, so you can see the effect of a smaller aperture. For new users, the immediate obvious effect is that everything gets dark; the increased DOF is more subtle.)

One possible solution is to replace the viewfinder screen with one designed for manual focus, possibly with a spilt-prism focus aid. Katz Eye is one popular brand, and there are a number of cheap Chinese import options as well.