The tvservice command does not consistently sense when HDMI is disconnected. Say you boot the Pi with HDMI, then manaully disconnect the HDMI cable. The tvservice command will still report that HDMI device is connected, in that -n, -s, etc. commands still report the last previously connected monitor via HDMI.
You can run the X server without the desktop, which then appears as a featureless black screen. Although there is no taskbar or menus, you can still start applications remotely (to do this via you need to set the $DISPLAY environment variable properly first), and/or at startup.
> export DISPLAY=0.0
If there is only one instance of the X server ...
I've faced a similar issue. In my case, I changed the DVI adaptor and everything worked fine. Apparently, the DVI adaptor was working fine with other electronics but when I used it with the PI I got the same warning as yours. So,
try changing the DVI adaptor.
Hope, it helped someone.