Unlike receiving email, sending email does not require a password. In fact, you don't even need an email address to send email. Just access to a server. Which means that anyone who wants to try to remain anonymous or otherwise cause problems can try to send email using another service's SMTP server. This problem has also been known to affect people using a mail server on their own local computer.
Users running their own mail server over a dialup connection is a common source of malicious email.
This is unauthorized relaying. While there are benefits to using one's own computer as a mail server, this is a violation of many IAPs' acceptable use policies, and should be avoided when communicating with other Internet hosts. The sender should always use the SMTP server belonging to the Internet Access Provider they are currently connected to. Relaying through third-party mail servers, regardless of whether or not the sender has a legitimate account there, should be avoided. One can attempt to confirm that this is their by problem via the AOL web site.