Are consumption taxes more equitable?

There is no doubt that consumption taxes are more efficient that labor income or capital income taxes, because they do not punish activities one would like to see promoted in an economy (labor supply, investment). But they are widely regarded as unfair, as the consumption share of income is higher for poor people. Hence the implementation of exclusions for essential goods where consumption taxes exist, in order the achieve some tax progressivity.

Isabel Correia claims that switching from income taxes to consumption tax can lead to less inequality even in the absence of lump sum transfers. This is a very counterintuitive result, and this is probably the reason why it made it into the American Economic Review (Yes, I know, I am breaking a trend here). But despite my best efforts, I still do not understand how this could happens, and the article provides very little in terms of explanation. Not only is no intuition provided, but the idea of using Gorman aggregation to reduce the model to a representative agent model seems wrong in this context. If anybody has read and understood the article, please help me here.