Hi Apple, yes you are right! Doing something unapologetically, if we look at the word, means doing something without apologizing: without saying sorry,regretting it, or justifying your action. Generally it means without caring.
Hence, when "unapologetically being yourself" it means you aren't caring about who other people think you are- as you said, you aren't ashamed of being yourself! It is a phrase that has more positive connotations, of empowerment.
Hence labeling positive things as being done unapologetically is like giving praise, but describing 'neutral' actions as unapologetic just means they are being done without care.
E.g. "She looked at me unapologetically" = "She looked at me without caring"
Hope this helps :)