Bring 6 quarts water to a boil and add salt. Cook the pasta according to the package instructions, until just al dente, and drain, reserving a little pasta water.
Meanwhile, in a 12 to 14-inch saute pan, heat the oil until smoking. Add the shallots, garlic, and crushed red pepper and saute until golden brown, about 4 to 5 minutes. Add the wine, bring to a boil, then add the butter, and remove from heat.
Add the drained pasta to the pan with the wine mixture and return pan to heat. Add crab, radicchio, and scallions and toss until radicchio is wilted, about 1 minute. Pour into a warm serving bowl and serve.