The common advice you mentioned is just a guideline and has little to do with how your portfolio would look like when you construct it. In order to diversify you would be using correlations and some common sense.
Recall the recent global financial crisis, ones of the first to crash were AAA-rated CDO's, stocks and so on. Because correlation is a statistical measure this can work fine when the economy is stable, but it doesn't account for real-life interrelations, especially when population is affected. Once consumers are affected this spans to the entire economy so that sectors that previously seemed unrelated have now been tied together by the fall in demand or reduced ability to pay-off.
I always find it funny how US advisers tell you to hold 80% of US stocks and bonds, while UK ones tell you to stick to the UK securities. The same happens all over the world, I would assume. The safest portfolio is a Global Market portfolio, obviously I wouldn't be getting, say, Somalian bonds (if such exist at all), but there are plenty of markets to choose from. A chance of all of them crashing simultaneously is significantly lower.
Why don't people include derivatives in their portfolios? Could be because these are mainly short-term, while most of the portfolios are being held for a significant amount of time thus capital and money markets are the key components. Derivatives are used to hedge these portfolios. As for the currencies - by having foreign stocks and bonds you are already exposed to FX risk so you, again, could be using it as a hedging instrument.