Two Mooney's have a critical encounter on the runway after landing opposite directions at a non-towered airport.

Narrative

Arrived at the destination airport in perfect VFR conditions. AWOS reported wind calm; 10 SM Visibility; skies clear. There were numerous aircraft on the CTAF announcing their distance from the airport and it appeared that my partner (flying) and I were number one for the airport. Arriving from the South; we announced and entered a left downwind for Runway 22. We observed no traffic ahead of us or anyone announcing a position ahead of us. I called left base and final for Runway 22 on CTAF. We were hearing numerous other aircraft announcing their arrival. We landed normally on the runway; which has several slight elevation changes along its length. Upon cresting the first elevation change; I observed another aircraft heading toward us. I took control of the aircraft and steered to the left side of the runway; as it appeared that the other aircraft was also heading to the left edge in the opposite direction. At that time I thought that the other Mooney was back-taxiing on the runway rather than on the taxiway. We passed each other in opposite directions without incident. I later encountered the other pilot and learned that he had actually landed on Runway 4. I told him (amicably) that I had not heard any transmission from him on CTAF. He said that he had been cleared for a visual approach to Runway 4 by Washington Center and stated he had heard no transmissions on CTAF. I believe that he hadn't changed from Air Traffic Center Control to CTAF. One cannot be too vigilant at any airport; especially when there is no operating control tower.