This trope is just not true, but people keep bringing it up when discussion of China's enormous debt growth comes up.
Chinese households might be less inclined to take on debt, but they've still managed to rack up about 30+% of GDP worth, so they are working on it.
You can lose your saving from currency devaluation. In order to pay off debt, a government can issue new currency (debt denominated in its own currency; in Eurozone countries they can only raise taxes and cut spending to pay off debt.) Your savings don't matter because there is so much more money. An old unit of currency is equal to new units.
We can't be certain of Chinese banks' liabilities but it is something you can keep an eye on in the Western press, if blocked locally ( http://www.bloomberg.com/news/2014-02-14/china-banks-bad-loa... )
If I was Chinese, I would not be too concerned as long as I did not have liabilities for my business or money deposited in a bad bank. If yes to either of these, you are at risk of losing everything.