Because Mongolia mattered at the time

Next, you'll be telling me that Abkhazia is a legitimate state because it's recognized by Transnistria and Nagorno Karabakh.
Did Mongolia "matter"? I suppose it depends on how you look at it. I was not, of course, trying to somehow argue that Mongolia could somehow force China to recognize Tibet as independent. But Tibet and Mongolia both have something in common--they were areas that were part of the Qing Empire, but areas that did not see themselves as "Chinese". When the Manchu Qing Dynasty was overthrown, many Chinese people wanted to create a new state for the Han Chinese, ruled by the Han Chinese. It was something explicitly different from the old, multi-ethnic empire of before.
Given the weakness of the Chinese state at this time, it is not surprising that many peripheral areas of the old Qing Empire tried to break away and form independent states. Mongolia, East Turkestan, and Tibet all tried this, but only Mongolia managed to attract any large degree of outside support. That's why I brought up the Mongolian treaty--it shows how one nation, trying to break away from the old Qing Empire, related to another nation trying to do the same.
It is true that Tibet was not recognized as an independent state by any major power during this time period, but the British Simila Convention shows that it was not seen as a "normal" part of China, either, the way that, say, Shantung Province was. As I said before, the Convention, which was signed by China herself (as well as Tibet and Britain), pleadged China not to "interfere" in the administration of Tibet. I think it is fair to say, then, that if China invaded and directly administered Tibet, it would be seen as a unilateral change in the status quo, at least. Given that Britain, the US, and China were allies during WWII, I don't think they would complain. But you seem to be implying that Tibet was seen around the world at this time as a part of China no different from any other, and that simply is not true. Tibet's status at the time was... complicated.