Yes, being a native speaker is extremely important, for a number of reasons.

While the level of English fluency in the general populace is quite low, there are a number of Chinese nationals teaching English in the PRC with exceptional levels of English. If some of these people, speaking English at fluent or near fluent levels as a second language, wouldn't qualify at a "native" English speaker, why should someone from Cameroon, India, or the Phillipines?

The market in China is dictated to provide students with intimate access to western culture as well as language. The fact is that this is what students and parents want when spending the high tuition foreign teachers salary's require. Most non-native speakers cannot provide this.

As is mentioned above, people like and want the American accent, even the British accent. No one wants to emulate Indian English intonations.

Consider yourself, as a foreigner living in China interested in Mandarin. Do you want your Mandarin teacher to be from Beijing or from Manila?

These are only a few of the most obvious examples. What I recommend to non-native speakers interested in teaching is to seek opportunities to teach your own native language.