We used ordinary least squares regression with country fixed effects
http://plosmedicine.org/article/info:doi/10.1371/journal.pmed.1001214#article1.body1.sec3.p3

Betrayed here is a lack of understanding of the relevant econometrics. The implication (unfortunately the model is not described precisely) is the new model, like the original, is dynamic, meaning that it includes the lagged dependent variable as a regressor. Dynamic OLS models with fixed effects on short panels like this one are biased; in fact it's called dynamic panel bias, and it motivated the design of the original authors' preferred "ABBB" regressions. As one might expect, there are trade-offs between the two models. But a good analysis would explain and think through the choices, and note in particular that the original authors' model is actually the more conservative one.