I guess you'd have to say that the word itself is illegitimate, as it purports to be a past participle of "to break," or perhaps "to burst," and clearly is not. But the usage has been around as slang for perhaps a century. The meaning of "to be caught breaking a rule" is much more recent.
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Anonymousis the word "busted" ever correct grammatically to use?Only when you are deliberately using slang.