The idea that social media platforms like Twitter are inhabited by vast numbers of social bots has become widely accepted in recent years. Social bots are assumed to be automated social media accounts operated by malicious actors with the goal of manipulating public opinion. They are credited with the ability to produce content autonomously and to interact with human users. Social bot activity has been reported in many different political contexts, including the U.S. presidential elections, discussions about migration, climate change, and COVID-19. However, the relevant publications either use crude and questionable heuristics to discriminate between supposed social bots and humans or -- in the vast majority of the cases -- fully rely on the output of automatic bot detection tools, most commonly Botometer. In this paper, we point out a fundamental theoretical flaw in the widely-used study design for estimating the prevalence of social bots. Furthermore, we empirically investigate the validity of peer-reviewed Botometer-based studies by closely and systematically inspecting hundreds of accounts that had been counted as social bots. We were unable to find a single social bot. Instead, we found mostly accounts undoubtedly operated by human users, the vast majority of them using Twitter in an inconspicuous and unremarkable fashion without the slightest traces of automation. We conclude that studies claiming to investigate the prevalence, properties, or influence of social bots based on Botometer have, in reality, just investigated false positives and artifacts of this approach.