To add some additional context as to why Chinese don't trust their banks, Bloomberg did a long writeup on the credit bubble problems over there [1]. TLDR: Chinese banks have ~$6.6 Trillion of outstanding loans to Chinese businesses who are increasingly unable to service the loans due to weak demand, which threatens to turn into a banking crisis.

[1]: http://www.bloomberg.com/news/2013-11-18/credit-driven-china...