The fact that the authors ignored potential heterogeneity in responses IS a problem for their analysis, but their result is still evidence against heterogeneous responses.

Why do you say that? Did you look at the data?

They found F values of 0.77, 2.161, and 1.103. That means they found different behavior in the two groups. But those F-values were lower than the thresholds they had computed assuming homogeneity. They therefore said "We have rejected the hypothesis", and claimed that the evidence, which interpreted in a Bayesian framework might support that hypothesis, refuted it.