The claim is the authors opinion. It’s a blog post not a study. I believe is he correct. Paid security audits are indeed broad and rarely deep.
The reason why is so obvious to anyone who’s engaged in them that what you’re asking for is like demanding a study that restaurants are more crowded around lunch time.
Paid security auditors must deliver vulnerability findings. The end. Deliver findings, get paid. Failing to deliver findings means not getting hired by that client again, or, in the case of bug bounties not getting paid at all. It really cannot be understated that if you are a professional auditor sitting at some client site you absolutely, positively need to be adding findings to the report. If you develop a pattern of not finding things then your colleagues will not respect you or want to work with you anymore.
Therefore, it is only rational to look broadly at the target for common classes of bug. There just isn’t time to deeply understand the target, and it’s foolish to try when everyone else just looking for common mistakes gets more findings and by virtue is more productive/valuable than you.