If a user restricts the default shared document library security on their personal site, as an administrator I can see the actions property - I do not see: New, Upload or Settings for that library like I do for mine and others whom did not secure.
Isn't there a way the administrator (me for entire site collection/mysites) can override this or view?
What do you mean you are an administrator? What type of admin access do you have to SharePoint? Has full control been given to you from the web application policy for that zone in central admin? Or has the user granted you to be a site collection admin on his/her mysite?
Based on what you are seeing, i don't think either of the above is the case. My guess is you are either a domain admin, used to seeing and doing anything you want or are a site collection admin on a different site collection. Even if you are a sharepoint farm admin, that doesn't grant you the access you need.
