Why do i have to pay tuition for fairfax county public schools?

I come from a pacific island called palau. I live in Alexandria, Virginia with my sister who is my legal guardian because I am underage, and my problem is that I am having a hard time enrolling for the public high schools here because I don't have my parents here with me even though I live with my sister who has complete legal authority to be my guardian. So when I went to the school I was trying to apply for called Mount Vernon High School they told me that I have to acquire a letter from my parents back in palau that they are ill, poor and all these stupid stuff to prove that they can no longer support me. This letter will be used to determine if I can attend Mount Vernon tuition free or not. Otherwise I have to pay $60 tuition everyday I go to school and that's crazy! $60 everyday!!! it's a public school! aren't public schools suppose to be free? Now I have to write a lying letter for the court that my parents are poor, and sick and can no longer support me because they didn't not approve of my parent's doctors letter. Sorry for the bad unorganized writing! When I am mad I write in an informal manner.