Well I've finally got some clear information and here it is.
To begin at the beginning, I originally sent in a support ticket (before starting this thread) as follows:
The answer came back that there is no way I can switch off auto-renew, and I must cancel the service in the panel on the date I wish the service to stop. So then I tried that, with the result described in the opening post of this thread. At bobocat's suggestion I then sent in another support ticket, but the reply was unclear. So I then sent in a third support ticket, as follows:
and finally a clear reply has arrived:
So Dreamhost allows one day on which I can cancel my hosting plan without penalty. If I forget on that day, or if I don't have internet access on that day, then they will re-bill me for a year of hosting, which of course I will refuse to pay. (I have already deleted all my hosted domains and linux users). Then presumably my account will go into delinquency and at some point my panel access will be blocked, and I will no longer be able to manage my registrations. (As a precaution, I have already transferred all my registrations away from Dreamhost).
Is this really the way it has to be? I think it's crazy.