I think that's a good explanation, and one of several correct ones. As for me—while the phrase always serves as a negation—the first thing that springs to mind is the meaning: "if I had to say something/anything." Possibly "That's not going to happen, if anything happens, it'll be this," also.
Or, outside of that, "if anyone should say anything, I should say so," possibly. Maybe?
(This is all spoken from the point of view of a Canadian. If I was innacurate, I apologize. I apologize for my atrocious Japanese.)