Thanks.
I first tried the obvious way, by switching off the option through the Tweak
Tool, and got this grey background. That's why I tried to fix it through
dconf-editor, but what seemed to be the relevant option there
(org.gnome.desktop.background draw.background) is commented as "deprecated
and ignored". Doing some research I found out that nautilus was involved. At
the moment it seems that nautilus has to be controlling the desktop for the
background image to be proplerly displayed, and that deactivating icons on
the desktop also takes the control of the desktop away from nautilus. I could
not find what the fallback is (i.e. who's in charge of the desktop if not
nautilus), so I did precisely what you are suggesting.
NB: the "Have file manager handle desktop" option is not available in this
version of the Tweak Tool, hence my guess that it might be set according to
the "show icons" option.