When checking the permissions on their user profile in SharePoint Admin, this is all correctly set which makes this even more - strange...
To resolve this problem you will need to access the user's user profile. To get there browse to:
SharePoint Admin -> User Profiles -> Manage User Profiles, then search for the affected user. Hover over the user profile that you need to correct then click on the drop down arrow and then Manage site collection owners. Change the Primary Site Collection Administrator and Site Collection Administrators to another account (preferably the account you are using to administer Office 365). Make sure that the affected user is NOT listed for any roles. Once done, apply the change. Then go back into the Manage site collection owners again and change the roles back to the affected user.
This should fix the problem that should never have happened in the first place!
TLDR: In SharePoint Admin; change the affected users user profile site collection admins to another user and make sure the affected user has no roles. Then change the site collection admin roles back to the affected user.