If it's hard coded in there as "basic" then that's what you have to do. There is a web.config key which will allow you to switch it across the site but I don't believe that works for those hard coded ones.
Another option is to go into the config file for the CKEditor and set the properties of the basic to that of the full tool bar. I've done this hack before and it seems to work but then all "basic" toolbars are now full.
I'd report your findings to Kentico and have them switch it out to use the web.config key instead.