Inference using Fisher's method

Fisher's method returns a p-value telling you if at least one of the null hypotheses should have been rejected. The key words here are "at least one".

Consider an example where you are testing the effectiveness of a certain diet on weight loss. This diet has been studied by multiple researchers in different settings, but all are testing the null hypothesis that the diet does not induce weight loss. All researchers report their p-values, and you use them in Fisher's method. Why would it make sense to reject some, but not necessarily all, of the null hypotheses?