In one of my help desk calls, someone asked why a user who only had Contribute permission seemingly had a ton of other higher level permissions associated with their account. Being the cynical IT person that I am, my first thought was “OK, what did they misunderstand?” However, looking at the following, I had to agree that they had a lot more than Contribute:
In 99% of the times I’ve used Check Permissions, I don’t see “The following factors also affect this level of access for” section. What’s worse, I didn’t know right off WHY this person was getting that additional information. It certainly wasn’t as part of their SharePoint permission group settings.
It took me a bit of time to finally figure out what the difference was. This particular person was originally put in the Site Administrators area for this site, as they were one of the original business owners. Roles shifted and their permissions were altered to only have Contribute, but no one removed him from the Site Administrators group. Once I did that, all the “following factors” disappeared.
SharePoint Duffbert 
This was very surprising for me, one of the user had complete access to Sharepoint libraries, which even he wasn’t aware of. Thanks for the post, which gave me clue to fix it.
I was able to remove his access, when I removed “Company Administrator” from Site Collection Administrator Group.
In Site Settings -> Under Users and Permissions -> Site Collection Administrators group, I removed “Company Administrator”
I use Sharepoint O365.
I was wondering how to get rid of those extra permissions. Would not have guessed to check the administrators group, but that’s exactly what it was. Thanks!