Weighing these 2 issues, my present gut feeling is that I should not take any action if the vacation program is only sending *one* response to each poster ...
I disagree. The subscriber is running software that harvests addresses of posters to the list and sends them unnecessary, unsolicited, impersonal, off-topic email. Once per poster is too often. You should shut the subscription off as soon as you find out it's happening.
It's not totally irrelevent that the motivation was thickheadedness rather than malice: when you tell the dodo why its subscription was suspended, your phrasing should take that into account, and if it's a first offense you should give the goof a second chance [contingent on an oath to use properly behaving vacation software or none at all]. But I'd say no, do not let it continue for the rest of the vacation. Many of those programs will send one vacation notice per "sender" per day rather than per absence, so tomorrow they'll be sent not only to posters who were quiet today but also to those who posted today and already got the big news.
If it recurs during a future absence, ban the jerk.
