However, all Chinese languages use the same written representation, so any Chinese person speaking a dialect of Chinese that is literate is as literate as a Mandarin-speaker.

This is doubtful as well, because the standard modern written language is based on the vocabulary and grammatical structures of Mandarin. (I am well aware of this, as someone who has lived for years in places where Mandarin is the official language, but the home language of most elementary pupils is a non-Mandarin Sinitic language.) A fairly detailed response to the claim that Chinese characters provide common literacy for people who can't understand one another over the telephone can be found in

http://www.amazon.com/Chinese-Language-Fantasy-John-DeFranci...

or

http://www.amazon.com/Ideogram-Chinese-Characters-Disembodie...

For your convenience, I can link a deep look into one of those books through a focused search on Google Books:

http://books.google.com/books?id=fRqKreZFVTYC&pg=PA10...