sendmail doesn't have to be a running process to be called by php.
php -i |grep sendmail
sendmail is actually 'split' ... one for localhost (submit) and one for sending/receiving (true sendmail) to other systems. Is your root user getting any system emails/notifications? That would be useful me thinks! Might install alpine to see.
Depending upon how hosted, it is possible for an internal network to have an internal mail server for all port 25 traffic - no smtp setup required.
Look at the full header of the message you did get, reading from subject line upwards to the top of the header. Think you will see phpmailer which is built into moodle.
However, can turn off any email using a line in config.php file.
$CFG->noemailever = true;
'SoS', Ken