[crazygringo]

First of all, that's not what perfect pitch is -- it is rare, but it has absolutely nothing to do with how well you can carry a tune.

But secondly, if the entire population of China can do it, then statistically, you're almost guaranteed to be able to do it too. And the tones in Chinese are really very, very simple. They're no different from the way you end a question with your voice moving upwards, or the recognizable "valley girl" pattern. It's the same idea, just applied to single words instead of whole sentences.