Just about all the people who've ever told me they were smart turned out to be dumb, whereas the people who called themselves dumb were almost always smart.
Anybody I've ever known who frequently said, "I'm not stupid," was in fact dumb. If they said, "I'm not naive," they were usually exactly that. And if they said, "My mama didn't raise no fools," their mama raised nothing but.
On the other hand, the type who makes a mistake and then immediately wails, "I'm so stupid!" is usually pretty smart. "I must be an idiot" usually signifies the opposite. And an utterly abject, mournfully delivered, "I must be a complete numbskull" is never spoken by anyone south of 130.
I knew one guy in college who would occasionally shrug and say, "I just don't have the brains these other guys do." I don't know what his grades were, but he was certainly far wilier than most of the nerds he was surrounded by.
The writer of this post, by the way, is extraordinarily intelligent.