When you want to purchase an ETF, you usually go to the secondary market where buyers and sellers congregate. When the purchase amount is significant, however, it needs to be created through the primary market and the way this is done is through one of the designated brokers that deal directly with the sponsor in the primary market. The broker uses the investment cash to purchase a basket of stocks that reflect all the constituents and their respective weights of the underlying index. This is then exchanged against an equivalent number of units of the ETF. In the event of a redemption, the exact opposite happens, whereby the broker exchanges units of the ETF for an equivalent basket of stocks representative of the index. Now imagine a bear market scenario where a whole lot of redemption activity is going on. In the case of a broad market index ETF, the broker will have to liquidate a large number of stocks right about the same time. In other words, all the constituents of the index will be experiencing selling pressure at around the same time which means an increase in the correlation between them.
This estimated general increase in correlations has led to a situation where you need to hold a larger number of stocks to achieve an optimal level of diversification. It also further emphasizes the importance of ensuring a broad level of diversification between different asset classes.