I know that debt is sold, pennies on the dollar, to collection agencies. The collection agency is then in a position to negotiate the debt and turn a profit on the transaction. That's their business model.
I am not sure that paying the collection agency does anything positive for the debtor's credit score. Given the bigger economic picture, laws and FICO score computations are changing daily to encourage debtors to settle. So what was, is apt to change ( for the better) going forward.
I am assuming they sent your daughter a form letter to sign authorizing the debits. The fine print may or may not contain language about their ability to also debit a collection or transaction fee. The devil is always in the details.
The whole deal makes me uncomfortable. Google the name of the collection agency/address and " scam" and see what comes up.