Bring 2 quarts water to a boil over high heat; add potatoes. Simmer until potatoes are tender, 15 to 20 min. Drain and immerse in cold water. When potatoes are cool, drain well. Soak onions about 15 min. in cold water to cover. Drain and mix onion with rice vinegar. Cut potatoes in quarters; add to onions. Trim tender watercress sprigs from stems, then finely chop enough of the coarse stems to make 1/2 cup. Mix chopped stems with potato salad. Mound watercress on a large platter with potato salad along side; cover and keep cool. Rinse salmon and pat dry. Place, skin side down, on a piece of heavy foil. Cut foil to follow outlines of fish, leaving a 1" border. Crimp edges of foil to fit up against edge of fish. Mix soy sauce with brown sugar and brush onto fish fillet.
Lay fish on center of hot grill. Cover barbecue and cook until fish is barely opaque in thickest part, 15 to 20 mins. Transfer fish to a platter with salad. Add salt to taste. Server hot or cool. Makes 6 servings.