I agree with your second statement, but your first statement doesn't necessarily follow, it depends on the proportion of jobs that are bullshit....
If a human is 1% likely to think a not-bullshit-job is bullshit, and 10% likely to think a bullshit-job is bullshit, but 99% of jobs are not-bullshit, then for every bullshit job that the worker thinks is bullshit, there are 9.9 not-bullshit jobs that the worker thinks are bullshit.
Your hypothetical would lead to roughly 98% thinking that their jobs are not bullshit when 99% actually were. At that level we wouldn't be having this discussion at all.
The actual numbers are more like 60% non bullshit / 40% bullshit, though.
Humans have an innate desire to be useful.