You are right that correlations among assets vary over time. If you think
now is bad, consider the 70's when the correlation btw US stock and US bonds
was around 0.6-0.7 instead of a negative number. This simply reflects the
randomness in the returns of these assets. In the long term, however, bonds
are still effective diversifiers against stocks. Also, we should consider "
magnitude", that is when assets become correlated than usual, the magnitude
of price movements differs. Almost always, bond prices are less volatile
than stocks. Lastly, the decision to go with index investing for many
passive investors is based on a humble realization that I, the investor, don
't have the ability to time the market.