Where is the trade-off?

This is the link to the article, “The fallacy of the equity-efficiency trade off: rethinking the efficient health system” by Reidpath et al. The international health literature, as all of us know, is replete with discussions of this delicate balance between attaining efficiency in health care delivery and equitable health gains, which is a problem that every health system needs to juggle with. However, this thought provoking paper brings out the inherent illogicality of this debate and presents an alternate view that the real trade off is actually between maximizing health gains and fair distribution of health gains for a given input. Surely, does this not provide a new perspective in setting better goals in resource poor settings?
http://www.biomedcentral.com/1471-2458/12/S1/S3