Bring a large pot of salted water to a boil. Add the linguine and cook until al dente.
Meanwhile, heat the olive oil in a large skillet over medium heat. Add the garlic and red pepper flakes and cook, stirring, until slightly toasted, 1 to 2 minutes. Add the capers and olives and fry 2 more minutes. Crush the tomatoes into the skillet with your hands and reserve the juices. Cook until the tomatoes are slightly dry, about 2 minutes. Add the reserved tomato juices, the basil, and salt to taste and cook until the sauce thickens, 1 to 2 minutes. Add the tuna with its oil, breaking it up with a fork, and season with salt.
Drain the pasta, reserving 1/2 cup cooking water, and return it to the pot. Add the sauce and the reserved cooking water and toss. Season with pepper and garnish with more basil.
Per serving: Calories 524; Fat 16 g (Saturated 2 g); Cholesterol 6 mg; Sodium 641 mg; Carbohydrate 73 g; Fiber 7 g; Protein 24 g