Long ago I read an essay by a psychology grad student claiming that it was a routine matter for statisticians to publish articles identifying a particular statistical error and listing a hundred psychology papers in which it occurred. Whenever this happened, the psychologists would immediately check the bibliography to see if they were tagged. They accepted the authority of the statisticians and were quite embarrassed to be caught, but this did not appear to affect how they did experiments or wrote papers, except perhaps avoiding already identified errors.

Can an academic psychologist comment on what happens?
Whether statisticians routinely publish criticism of psychologists that is noticed and accepted seems a pretty concrete fact that everyone should agree on, unlike the dynamics that Dan speculates, which could be opaque to those engaging in them.