If HR has been informed that you are spending non-work hours with a known thief, it would be right to question your judgment. If the job to which you might be promoted requires good judgment, then officials might see that as a reason not to promote you.
Unless you are in a unionized environment that has specific seniority guidelines for promotions, the company management can promote whomever it chooses. What you are really asking is not whether your
employer has the right to know what you do when you are clocked out, but whether management should depend on a rumor in making a decision that affects your career and pay. And the answer to that is that it should not.
Have you told your employer your perspective on this matter? If not, do so calmly and showing that you are sincere. Tell them that you have not been fraternizing with the person in question and that you feel that you have earned their trust and deserve the opportunity for advancement.