From reading the report, I believe that one of the reasons that the British sided with the Muslims is because the very idea of "ownership" of the holiest place on the planet was so totally repugnant to the rabbis who testified as to its Jewish character:
The Jewish Side do not claim any proprietary right to the Wall. The Jewish Counsel are of opinion that the Wall does not constitute a property in the ordinary sense of that word, the Wall falling under the category of res divinum or res extra commercium. On the basis of that point of view the Jewish Side protest against any and every form of innovation in the structure of the Wall and its immediate surroundings carried out by the Moslems. The Jewish Side have submitted to the Commission a detailed "Note on recent Moslem innovations at the Wailing Wall," which is annexed to this document (Appendix XI). The plaintiffs refer to a pronouncement made by Sheikh Hafez, when he was examined as a witness before the Commission, with reference to the properties dedicated as Waqfs (pages 711-712), to the effect that some learned lawyers and some jurists would say that such property is the property of God while some say that it is the property of nobody. In this connection the Jewish Counsel ask the Commission to accept the above definition which would have the advantage of solving entirely the problem.In other words, the Jews' intense knowledge of the extreme holiness of the Temple Mount was interpreted by the secular British as an admission of non-ownership, thus strengthening the Muslim case.
The Muslims, on the other hand, had no problem claiming complete ownership:
It is here a question about property which has belonged to the Moslems for many centuries.
Obviously, from a legal perspective the Jewish claim was not the best argument, but it proves beyond a doubt to whom the area is more important.
But interestingly, the current Arab claim that the Wall is theirs under international law based on this document is contradicted by their very own words in the document itself:
The Palestine Arab nation have rejected continually and in every opportunity the British Mandate over Palestine, and therefore they cannot be bound by any arrangement or regulation derived from that. Mandate; nor can they be bound by anything pertaining to what is known as the national home policy. My statement in this direction should not be taken as indicating any departure from that attitude which was adopted by this nation in exercise of its right to determine its own future.The Muslims, in their arguments before the Commission, already said that they do not consider the Commission to have any legal right to determine anything. It is rather hypocritical for them now to claim that they have the right to the Wall under international law when they themselves explicitly reject that document itself by their own words in this very report.
Second: Moslems state that all contentions relative to Moslem sacred places should be dealt with only by competent bodies as prescribed by the Sharia Law. Other bodies can have no jurisdiction whatever by the Sharia Law. Other bodies can have no jurisdiction whatever on these places.