> They have every right to question you.

Sure, but they have no right to issue you a ticket without proving you broke the law. Same as in the gun case: they have every right to question you, but they can't convict you for murder based solely on evidence that it was your gun that killed the victim.

A ticket (citation) is a promise to appear before a court, not a conviction of anything. Law enforcement can cite anyone with only reasonable suspicion than a crime or infraction has been committed.