From this document, http://quantlabs.net/academy/download/free_quant_instituitional_books_/[JP%20Morgan]%20Variance%20Swaps.pdf, on page 56, it states that
Losses from short correlation through variance dispersion can occasionally be very large, especially since the trade becomes short volatility following adverse moves in correlation.
I cannot see how short correlation through variance dispersion becomes short volatility.