STATISTICIANS actually do fine, generally. The problem is that no statisticians were involved in the analysis and write-up of almost all research that isn't statistics papers.
The statistics just don't mean what most scientists think/write they mean. They're using em wrong. As the OP explains some manners of, in fairly technical language.
Statisticians are doing fine indeed. The problem lies entirely in the ( non) design of experiments ( DoE) of the “scientists”. The sorry state of affairs of graduates from universities in properly designing experiments in which proper randomization, focus on sources of variability, between groups and within groups is not understood nor accounted for in the design is the true source of the problem. Scientists should always consult a statistician when undertaking an experiment. At least if they would like to make/draw sensible conclusions.
Yes, I was just saying along with OP that a statistician would be most critical of the professor's reasoning. It's like a tyrant saying you should take a class in morals when you raise an objection to their atrocities.
The statistics just don't mean what most scientists think/write they mean. They're using em wrong. As the OP explains some manners of, in fairly technical language.