As a non-native speaker I say that there is a huge difference between speaking/writing fluent English and doing this in a way that satisfies "unwritten cultural conventions".
For my English, for example, native speakers tend to say that it is actually quite correct, but I have a tendency to use words in a specific way in which few native speaker would use them.
I am a non-native english speaker too; I guess I bristle at the the reading that this man isn't in control of his english when he writes with obvious proficiency, a reading I suspect, would not at all be in question were his name John Foster Edwards, or Henry Wickham or whatever Anglo-Saxon name you wish to replace his name with.
I see your point though. I think he does use words in ways that native speakers do not use, but in his anecdotes -- I think he's actually playing up his Chineseness for the comic effect, and he's very much aware of what's happening.
For my English, for example, native speakers tend to say that it is actually quite correct, but I have a tendency to use words in a specific way in which few native speaker would use them.