1. We agree on the British non-claim to Palestine. Actually, so did the British government. Only the original poster thought otherwise.
2. The Ottomans usually claimed and had some control of eastern Arabia (where Mecca is). They nominally claimed the west (from which the Saudi came) but until the oil discoveries, that part was basically “hefker” from the point of view of national governments.
3. Balfour never promised an independent state. At most, contemporaries thought it might involve a self-governing entity similar to what Canada or Australia were at the time (no control over military or foreign affairs, financial matters controlled from London, judiciary controlled from London, all decisions subject to review by London’s governor). Given that at the time, Palestine wasn’t British territory, the concept of a “homeland” wasn’t tied to sovereign status in any form – only a place where Jews could move with no guarantee of political control. They also promised the Arabs a state in the region, which led to the famous Faisal-Weizman agreement, and also to De Haan negotiation with Faisal (the idea being the autonomous Jewish homeland with a large Arab state – sort of a Dhimmi/ghetto on steroids – but enough so Jews fleeing Europe could have fled, and the Brits and Americans would have been less resistant to helping Jews flee Hitler).
There were no “Palestinians” before 1948, only a group of “Levantine” Arabs including all of modern Jordan, Lebanon, Syria and Israel. It would have been a lot easier for a country that was 90% Arab to tolerate a Jewish minority that wanted authonomy and economic freedom, than for a small Palestinian entity to accept being part of a country with a probable Jewish majority – Muslims don’t take kindly to being a minority – something that the rabbanim realized which is one reason they opposed zionism (if we try to boss the Arabs around, it guarantees war).