It is voluntary to enter into a payment plan--the creditor (i.e. the hospital) does not need to agree to let you pay over time. Since it is voluntary on their part, they may put any limitations or terms or conditions on it that they like, such as that you will enter into a contract or agreement with them regarding repayment. In fact, payment plans are commonly or normally reflected by and memorandized in written agreements--it is unusual that you have not encountered that before. If you do not sign their agreement, they could put you into collections and/or sue you for the money.