In a large saucepan, cover the wild rice with the water, add 1 teaspoon of salt and bring to a boil. Cover and simmer over moderately low heat until the rice is tender but still chewy, about 1 hour. Drain the rice well.
Meanwhile, heat the oil in a large nonstick skillet. Cook the garlic over medium-high heat until golden brown, about 2 minutes. Add the greens and cook, tossing occasionally, until wilted, about 4 minutes. Add the balsamic, red pepper and season with salt. Cook one minute more, until the vinegar has reduced, and remove to a mixing bowl.
Toss the wild rice with the wilted greens and serve warm.