Because of the Chinese Civil War (which technically never ended), both the government of Taiwan (under the name "Republic of China") and Beijing (under the name "People's Republic of China" claim to be the 'real China'. At some point in time, most people recognized the Republic of China as the legitimate government of China, however, as the situation stagnated and the relevance of China became more important, most countries now recognize the People's Republic of China as the legitimate government of China.
As for the NATO question - no, no such rule exists and nobody would want such a rule because it is a defence pact.