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 crushed red pepper 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 of the cooking water, and return it to the pot. Add the sauce and the reserved cooking water and toss. Season with black pepper and garnish with more basil.