I don't see the difference between Tibetan independence in 1913 and other provincess independence in other years, earlier or later. The fact that they declared independence, from foreign political entity is the point. However, we'll never say there were dozens of countries in China then, since a country is not that easy to found. As for Jiangxi's independence declaration, the citation I quoted is politically sufficient I  think, since Tibet's independence declaration is not precisely correct in modern terms.