It's hard to say what goes wrong with the information you give. One possibility is that the user account you sign in with is a "Site Administrator" or "Site Owner" - in this case, they'd have permission to administer content in that site by default. If you make that user account just an ordinary "User", the permissions should disappear.
If you have custom roles, note that the "Define Permissions" section for roles has multiple occurrences of "Web Content": See the intermediary headers for "Content", "Applications" and "Control Panel". You'll find the relevant parts in the "Content" section.
Page permissions have nothing to do with permissions to content like WebContent.