Preheat grill to medium heat and lightly oil the grate.
Season salmon fillets with salt and rub lightly with oil.
Place salmon on the preheated grill; cook salmon for 6 to 8 minutes per side, or until the fish flakes easily with a fork.
Combine water, rice vinegar, brown sugar, chile paste, ginger, garlic, and soy sauce in a small saucepan over medium heat. Bring mixture to a boil, then reduce heat to medium and simmer about 2 minutes, or until slightly thickened.
Sprinkle basil on top of salmon and spoon glaze over basil.