The purpose of the overpressure valve is to provide a safety in case of first stage failure, not failure of second stage. Should the first stage fail, and this is typically a small leak, air is vented from the valve and not through the second stage (mouthpiece). The diver can usually complete the dive without any disturbance to his breathing cycle.
Single hose, upstream designs use a tilt valve. The only failures of even remote likelihood would be a broken spring or damaged valve seat. I don't see how either of these could lead to shut off of air. Once the diver inhales against a broken spring the valve will jam open similar to the 'downstream' mechanism. Similarly, a damaged seat will cause a leak in either type.
The DIR people claim to avoid excess failure points and I can see that an overpressure valve might fail due to corrosion or whatnot. However, I feel that this is an exaggerated concern. This component is no more likely to fail than a piston regulator which is also subject to flooding. In addition, the downstream valve associated with this type of regulator is subject to tiny wear indentations which can lead to chatter or hard breathing or leaks. The upstream valve is not subject to this problem, to my knowledge.
It may be of interest that the typical diaphragm FIRST stage is an upstream design.