Does the broker have a right to commission when the owner leases their unit directly, after the prospective tenant initially refused to pay the broker's commission?

The broker is entitled to his agreed-upon commission upon completing his work. According to the question, his work is completed by booking the apartment, not merely by pointing it out. Therefore, if the broker informs that there is no reservation without payment, he has not accomplished the work for which he would be entitled to the full commission. He is only entitled to a customary fee for the referral. However, if it is customary for his work to be completed merely by pointing out the apartment and its owner, then he is entitled to the full commission.