AN ACR MLG AND A CPR MLG BECAME NOSE TO NOSE WHILE TAXIING IN THE FOG AT DTW.

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WX AT ARPT WAS VERY FOGGY. RPTED VISIBILITY ON TKOF RWY WAS RVR 800 FT. ALTHOUGH VISIBILITY AROUND ARPT VARIED SOMEWHAT; I DON'T THINK VISIBILITY WAS BETTER THAN 1/4 MI ANYWHERE WE TAXIED. GND CTL INSTRUCTED US TO TAXI E ON THE INNER; R AT OSCAR 4 AND W ON THE OUTER. AS WE STARTED A R TURN TO TAXI; WE WERE CONFRONTED BY A CPR MLG TAXIING TOWARD US (WBOUND) ON THE INNER. WE BOTH STOPPED AND WE WERE ABOUT 300 FT APART AT THAT POINT. WE NOTIFIED GND CTL OF THE SIT AND THEY ASKED THE CPR MLG ACFT TO IDENT HIS POS AND HE SAID HE 'THOUGHT HE TURNED R ON THE OUTER.' GND CTL THEN INSTRUCTED HIM TO DO A 180 DEG TURN; TAXI E ON THE INNER; R TURN AT OSCAR 4 AND W ON THE OUTER. IF THE VISIBILITY HAD BEEN ANY WORSE; THERE IS A POSSIBILITY WE COULD HAVE HAD A CRUNCH. DTW METRO IS HEADQUARTERS FOR THIS CORPORATE FLT DEPT. IF THEIR PLTS HAVE PROBS TAXIING AROUND THE ARPT; WHAT CAN YOU EXPECT FROM US OUT-OF-TOWNERS? I GUESS DTW DOESN'T HAVE THE ARPT MARKINGS; SIGNS AND TXWY DESIGNATIONS WORKED OUT WELL ENOUGH TO PRECLUDE ANOTHER ACCIDENT.