Prepare a grill for medium-high heat; oil grate with vegetable oil.
Season fish on both sides with salt.
Pour 2 Tbsp. vegetable oil into a shallow bowl or a baking dish; add fish and turn to coat.
Heat olive oil in a small saucepan over medium-low.
Add garlic and saffron, crushing threads between your fingers, and cook, stirring occasionally, until garlic is just starting to turn golden at the edges, about 2 minutes.
Scrape into a medium heatproof bowl; set aside.
Grill fish until firm when gently pressed and opaque throughout, about 5 minutes per side.
Transfer to a platter.
Add tomatoes, chives, parsley, olives, and vinegar to bowl with reserved garlic mixture and toss to combine; season with salt and pepper.
Spoon over fish.
