I'm fortunate to work in a biotech startup where the CEO actively encourages people to push back on him and he seems to relish it. In fact, one of my colleague's unofficial job titles is "devil's advocate", particularly around statistical claims (e.g., anti-p-hacking).
It helps that the team members are all fairly experienced, have a previous history of working together, and are generally mature individuals. I'm not sure it works without that filter, which is possible for us because our CEO is a serial founder with a deep network of competent people.
You don't only need to think about literal p-hacking, think "If I was using Bayes would this still be a problem?" For a lot of the more subtle stuff, the answer is "Yes."
It helps that the team members are all fairly experienced, have a previous history of working together, and are generally mature individuals. I'm not sure it works without that filter, which is possible for us because our CEO is a serial founder with a deep network of competent people.