Double-blind trials aren't the gold standard, they're the best available standard. They still don't replicate far too often, because they don't remove bias (and I'm not just referring to publication bias). Which is why, when considering how to interpret a study, you look at the history of what scientific positions the experimenter has supported in the past, and then update away from that to compensate for bias which you have good reason to think will show up in their data.

In the example, past results suggest that, even if the trial was double-blind, someone who is committed to achieving a good result for the treatment will get more favorable data than some other experimenter with no involvement.

And that's on top of the trivial fact that someone with an interest in getting a successful trial is more likely to use a directionally-slanted stopping rule if they have doubts about the efficacy than if they are confident it will work, which is not explicitly relevant in Eliezer's example.