Why is the use of native speakers so important?

Can't a non-native fluent speaker of the target language produce the same translation as a native speaker of the target language?

Part of the correct translation process is the use of correct grammar and vocabulary. However, at the same time, the use of that grammar and vocabulary needs to be done in the right contextual circumstances, and under the right cultural conditions.

Native speakers of the target language are aware of such cultural conditions and under what context certain things should or shouldn't be said having lived under these conditions their whole lives.  Non-native fluent speakers of the target language are probably exceptionally proficient when it comes to grammar and vocabulary, but less than adequate when it comes to placing that grammar and vocabulary in the right context.

Let us consider a fictitious example of the problem of not using native speakers in translation. John Doe, and American college student, learns Mexican Spanish while living in Mexico for 3 years studying Chicano language patterns,and acquires a vast Border Spanish vocabulary.  Because of this he thinks that the Spanish he learned will suffice for translating a document from English to Spanish for an Argentine fruit company. As he translates he comes across the word "pineapple" which he unconscienciouslly translates to "piña" (the word that all Spanish-speaking Mexicans would use). However, unbeknownst to John, the Spanish word for "pineapple" that they use in Argentina is actually "ananá" and the word he uses means "a punch"(in the face!) Because of this mistake the Argentine fruit company loses thousands of dollars in revenue, due to the lack of correct translation. Now this is a made-up example, but you can see that fluency alone does not cut it when operating in a global, ever-changing language. Native speakers have that fluency, but are able to adapt that fluency to the cultural conditions of that particular country.