I've only been publishing and doing peer review for about 10 years now. The stat software has been available for that entire time. So I really don't have an opinion on whether it has changed. Part of the problem is that the peer-reviewers are, like the authors, usually specialists in the subject matter of the Journal and frequently are not strong in statistics.
The problem has been around for at least 40 years in my direct experience. Of course, Fisher claimed that Mendel faked data (and Dalton was similarly accused.)