Quoting Didier Kryn (kryn@???):

> In any case, any person who has the possibility to push the
> power button or cut the power cord should be given the opportunity
> to click the halt button instead. ctrl-alt-f1+ctrl-alt-del can be
> used to reboot, but there's nothing to halt.

Halt is accomplished by first doing ctrl-alt-f1, ctrl-alt-del, then
turning the system unit off before significantly into startup (assuming
physical access to the system unit in addition to a physical console).

Or, as you say, through a hardware button on the system unit, or yanking
the mains (AC) cord.

(Technically, you spoke of someone 'who has access to the shutdown
button of the display manager', which in edge cases _could_ be a remote
user -- but generally is not.)