They can attempt to collect on an old debt, the onus is on the debtor to exercise their legal right to "ignore" a bill past the statute, which varies by state, and by type of debt, note, etc.
http://www.bankrate.com/finance/savings/when-does-your-debt-expire.aspx deals with this issue. Of course they can try to collect, they just cant threaten to sue for one past the statute.
Mary didnt say any illegal tactics were used, just an attempt to get paid for the service they provided. However, once there is new activity on the account, a payment made, etc.. the statute of limitations is wiped out. It starts all over again. So if a person isn't going to pay a debt just because it is old, it is best to just throw them away without calling.
It is an honorable thing Mary and her husband are doing, by taking care of it, regardless of how long ago it happened. In some states, Arizona in particular, some hospitals are going bankrupt and closing their doors in part due to all the unpaid bills, particularly from illegals. People having to drive for miles to get to a hospital, especially if they live in a suburb or more rural area. Being in Texas, I see this often on the news.
On a humorous note.. I was telling my husband about this post, and the bill from a boy being circumsized, and he's a young adult now..and he laughed and said what will they do if the parents don't pay.. re-attach? (grin)