Their work shows that the method for managing volatility will have an important impact on skew and the relationship with other markets. The constant volatility approach will not have skew but will have the highest Sharpe ratio for their tests. The equity based volatility adjustment will have positive skew that will be tied to the equity market moves. It will have the highest crisis alpha or negative correlation during "bad times". The signal generated volatility will have the highest skew but the lowest Sharpe ratio.
Their analysis addresses some fundamental issues with trend-following. Conventional wisdom that all trend-follower will have skew is not always correct or may be right for the wrong reasons. The paper assumes that skew can be caused by mixed distributions, but the method that creates the mixture will have different implications for skew. The volatility management will matter.