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 Philippines?

Interesting point. However the history and usage of English is different in the Philippines, India and Cameroon, than it is in China.

In the Philippines, Filipino and English are the official languages. English has been used as the medium of instruction in schools in the Philippines for decades. This does not qualify Filipinos as native speakers but it would mean that they could rightly, generally claim higher salaries for teaching EFL in China than a Chinese national could. Please check the following sources:-

http://en.wikipedia.org/wiki/Languages_of_the_Philippines

http://au.answers.yahoo.com/question/index?qid=20061120030502AAwrslB

As we all know India used to be a colony of Britain. This colonization goes back more than a century, so the history of the English language has had a great influence on the people in India. English is the most widely spoken language in India after Hindi, and India still has the third largest English-speaking population in the world. Look at the following article to see how much talent there is in Indian society in the use of English. This is why Indian nationals with good English speaking skills are generally paid a higher salary than Chinese nationals who teach English in China. Again, please check the following link:-

http://www.chillibreeze.com/articles/EnglishinIndia.asp

The official languages of Cameroon are English and French. Part of the country was colonized by the British last century. The languages of instruction in schools in Cameroon are English and French. Please refer to Goerge Echu's article titled "The Language Question in Cameroon" (the link is below this paragraph), to see how widespread the use of English is in the Cameroon. This is why good English speaking teachers from the Cameroon will generally expect a higher salary than their Chinese national counterparts when it comes to teaching English in China.

http://www.linguistik-online.de/18_04/echu.html

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

I think the "Access to Western culture argument" as an argument for not using non-native speakers in China is pretty weak. Firstly, could you define what you mean by culture? The term "Western Culture", is very vague. What is "Western Culture"? Could you define it in more specific and detailed terms? Also are Chinese students learning a language or a culture? My experience of teaching English in China is that Chinese students are not REALLY interested in learning "Western Culture". They are just curious about some of the basic differences in the way we live in the West as opposed to China. Serious students of English in China are much more concerned that a teacher speaks English clearly, and fluently and teaches in a competent and interesting way, than whether he can teach "Western culture".

Although Chinese students generally profess a primary interest in Western culture, it does not mean that this is the only culture they are interested in. Switch on the TV. Take a trip to see cultural exhibitions and performances in parks, theatres and at concerts in China and see that Chinese people have an interest in people and countries all over the world. There are in fact indications that many Chinese people are getting slightly fed up of Western culture (which China has become swamped with in the last few years) and are increasingly looking further afield for something more exotic (for instance in Africa and South America).

This is also reflected in the interest students take in teachers of English from other countries outside the big five. Are you saying that Chinese students ONLY want Western culture? If you mean that they MAINLY want Western culture then surely there is still a place for non-native speakers of English to teach in China. In any case as I stated earlier the teaching of "culture" is not that important to Chinese students. It's more of a curiosity than anything else, and that curiosity extends to countries all over the world.

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

Chinese students may generally prefer to speak English with an American or British accent, but that does not mean that they are happy to have ANY American or English person teaching them English. While working in a chain English school in Beijing I personally witnessed two native-speakers (both white by the way)-one from England and one from America- rejected by the school because the students considered their accents too broad for them to understand. No-one wants to emulate poor sub-standard English uttered by native-speakers, either.
Students in China are increasingly recognizing that there are many non native English teachers who speak better English than many native speakers.

If I wanted to be taught Chinese I would not base my choice of teacher on nationality alone. It's interesting that you only gave the option of a choice of Chinese teacher from ONE city in China. Would you want your Chinese teacher to be a worker from a small village in Yunnan, or an educated person from Manila with good, fluent, standard Chinese speaking skills?

Because of the difference in history of the English experience between China and many other countries in the world, many English speakers from these other countries can expect higher salaries than their Chinese counterparts when teaching English in China even though they are not classed as native speakers. If someone comes from a country where English is the language of instruction at school, this would increase their chances of internalizing the language.

You mentioned the importance of "culture". Non-native English speakers have countries too. These countries also have culture, so they too can bring something fresh, interesting and new to China that Chinese nationals cannot.

As regards learning Chinese, I would prefer a competent Chinese native-speaker to teach me Chinese. However, If the Chinese language had a similar history in Cameroon, India, and the Philippines as the English language has, then I would certainly have no problem with a competent teacher from one of the above countries, who spoke standard Chinese fluently, teaching me Chinese.