Return of Title IV Funds

I withdrew from classes after receiving financial aid; because of the timing of when i dropped my classes, I was subject to the return of title iv funds policy. The school returned part of my financial aid that was unearned due to dropping glasses to the dept of ed. this left me with a balance owed to the school.

my question is...
do i owe the school? or the dept of education? because it was repaid by the school, as outlined specifically in their policy, to the dept of ed, it now appears that i owe the school, not the dept of ed. is that correct?
This is the policy from the school's website:

Return of Unearned FSA Funds

• The school must return the lesser of the following:
  
  
  
  • The amount of unearned FSA Program funds; OR
    
  • The amount of unearned institutional charges
    
  
  
• The student (or parent, if a Federal PLUS loan) must return or repay, as appropriate:
  
  
  
  • Any FSA loan funds in accordance with the terms of the loan
    
  • The remaining unearned FSA Program grant (not to exceed 50% of the grant) as an overpayment of the grant
    
  
  
• If a student earned more aid than was disbursed to him/her, the institution would owe the student a post-withdrawal disbursement which must be paid within 120 days of the student's withdrawal
  
• The institution is required to return the amount of Title IV funds for which it is responsible no later than 45 days after the date of the determination of the date of the student's withdrawal
  
• Students who have Federal funds returned as a result of a withdrawal and now owe money to the institution are notified by e-mail and a ???Balance Due Hold??? is placed on the account
  

Seems clear but still can't really get a straight answer out of anyone, and I am finding conflicting information online.