The first clause of the rule is, I think, what you are looking for in this case.
§ 4038.1. Who may make claim.
(a) Claims may be made by an owner licensed for the current year, or duly authorized
agent, if the owner is presently registered in good faith for racing at that meeting and
has nominated a starter in the previous or current race meet of the licensed or
franchised racing association, up to or including the race in which the claim is made.
Such claim shall be in the name of the owner making the claim, or in the name of the
entity of which the claimant is the managing owner.