This depends on the company, their policies, and the setup. Our users do not have the ability to remove admin access from files we can access. It seems like you learned to remove this as well. The people before me set that up before we learned that lesson the hard way. I cannot think of a good reason for a user to be able to edit their own file permissions, unless they were a technical person with a good understanding of the infrastructure. Changes to things like permissions should only be made by people who have a good business reason, and know what it means when they make the changes. But, at the same time, it needs to be possible to restrict administrator access. (Even though completely preventing admin access is not possible through ACLs, I think encryption can do it, but no user wants to risk us not being able to restore their data.)
There are two things I can think of that I should not have access to, one is EPHI, which is protected by HIPAA. I know I could access those files, but the ACL prevents casual admin access. The other might be financial data that is protected by SARBOX, I don't know the rules on that I just know the servers need to be locked down tight and I doubt the government regulations just trust the IT team to behave.
I ended up removing this from my original post, but the settings that prevent his access are one of two things, intentional or unintentional. Therefore, he should check with the owner of that information if he should have access. If he just goes ahead and forces his way past the settings that are preventing access, he is assuming that those settings are there incorrectly. If he is wrong it could be a big problem, depending on the type of data accessed.