Why is this right? Give the baton to he who is closest to you when you run by. Does the case of the restrictive clause drive the case of the sentence object?
Well, how about this?
Give the baton to he whom you trust.
It sounds worse to me than your example, so I'm guessing that you are right, and that "he" in your example is due to agreement in case with the "who" of the relative clause.