I could not access a page as administrator user
From hook_menu():


  "access callback": Defaults to user_access() unless a value is inherited from the parent menu item; only MENU_DEFAULT_LOCAL_TASK items can inherit access callbacks. To use the user_access() default callback, you must specify the permission to check as 'access arguments'


Emphasis mine.

So if you don't provide an access callback explicitly, user_access() is used, which, unless you're logged in as user 1 which is a special case, returns FALSE if you don't provide it with any access arguments. That's why passing in access arguments fixed it.

You can't change this default behaviour without changing core Drupal files. Being explicit about your access is better than being implicit anyway - default should always be to deny.