http://www.pnas.org/content/pnas/suppl/2018/07/31/1800097115...
The data appears to not be in the friendliest of formats (tables with an axis labeled 'X'? No way my professors would've let that slide).
Chart S1 plots the distribution of the predicted probability for survival in four conditions. The distributions for "Male Doc, Female Patient" and "Female Doc, Female Patient" are visually indistinguishable and peak at around 0.96. "Female Doc, Male Patient" peaks at around 0.97, "Male Doc, Male Patient" at 0.98 or so. The difference in the position of the maximum is real, but tiny; the distributions for female patients are much wider (which visually exaggerates the difference). The math seems to agree with my reading, as it says: "when physician gender (male / female) is regressed upon (ŷ), conditional upon controls, there is no significant correlation between ex ante probability of survival and the gender of the physician."
So, dear "Scientific American": It is completely untrue that "Women Die More from Heart Attacks Than Men—Unless the ER Doc Is Female". The data says that "Women Die More from Heart Attacks Than Men—No Matter Who Treats Them" and that "Men Die More from Heart Attacks Than Other Men—When the ER Doc Is Female"
No thanks for turning a study that found tiny differences into a politically charged statement.
But then why would Brad Greenwood, the author of the study, state that "All of those are statistically indistinguishable except for male doctor–female patient", when it's obvious to the naked eye that there are other difference? I guess one difference made it over the arbitrary threshold of significance, and others didn't. That's just the nature of SHIT (Statistical Hypothesis Inference Testing).