Recently when I tried to change the title of a list view through SharePoint designer 2013, I got the error message saying "You do not have permission to do this operation. Ask your web site administrator to change your permissions and then try again, or log on with a user account that has this permission.".
Also check out:
Here the list is presented in the sub site and I have full permission to the sub site (presented in the Owner group). But when I followed this Microsoft KB article
which says an user needs to be a member of one of the following groups at the site collection level to be able to use SharePoint Designer and modify SharePoint content:
- Site Collection Administrators
So modify through designer, an user should be presented in any of the above group.