In an ideal world, you would be right. In this world, I just read a study (that passed peer review), where they took per-capita data from a district with 100 people, data from a district with 50.000 people, averaged them without weighing by number of people, then presented the result as the per-capita average for all districts.

That is when they're not outright fabricating data, and having their colleagues cover for them (at Harvard):

In or before 2020, graduate student Zoé Ziani developed concerns about the validity of results from a highly publicized paper by Gino about personal networking. According to Ziani, she was strongly warned by her academic advisers not to criticize Gino, and two members of her dissertation committee refused to approve her thesis unless she deleted criticism of Gino's paper from it. - https://en.wikipedia.org/wiki/Francesca_Gino