This is perfectly fine. Not all fields have the luxury of perfectly controlled lab experiments. If we applied the methodological discipline of experimental physics to social sciences, we might as well give up now.
In the abstract they say:
"Despite this being a well-known and widespread social phenomenon, relatively few large-scale empirical studies have been conducted into this issue. This paper attempts to fill this gap in the literature by examining teenagers’ propensity to claim expertise in three mathematics constructs that do not really exist."
"we find substantial differences in young people’s tendency to bullshit across countries, genders and socio-economic groups"
"Together this provides important new insight into who bullshitters are and the type of survey responses that they provide."
In the conclusions they say:
"There are of course limitations to this study, and many issues on the topic of bullshitting that remain unexplored. First, the PISA data analysed are cross-sectional rather than longitudinal. We therefore do not know whether bullshitting is a stable trait that can be consistently observed for an individual over time, or if it is something that changes with age (and the factors associated with such change)."
Their strongest claim appears to be: "Despite these limitations, we believe this paper has started to open an important new area of social science research"