I do agree with you that people who are vaccinated may simply be getting tested a lot more, and when asymptomatic people are tested the false positive rate skyrockets (it can easily be over 90% due to low positive predictive value in low prevalence settings). People who are not vaccinated may simply be generally avoiding all of the pandemic hoopla including avoiding getting tested as much as possible. However, each study will of course specify the circumstances by which people were being tested and I imagine it's different for each study.