Angiolillo,
Sounds like someone's been drinking too much.
I've NEVER seen a DH 2 marked with a skull & crossbones (that doesn't mean there might not have been one, but it seems out of character with RFC marking practices on the Western Front at this time, and Hawker certainly never flew one).
There was a two-seat
D.H.1A that served with No. 14 Squadron during its service in the Middle East. Possibly there was a little more leeway regarding personal markings in this out-of-the-way theater, and several photos exist showing this D.H.1A with a white skull & crossbones painted on a dark nose (nacelle). Our own Colin A Owers included this in his superb book "De Havilland Aircraft of WWI, Volume 1: D.H.1 - D.H.4," and Juanita Franzi did a super four view illustration of this D.H.,1A, number 4609. The nose was interpreted as painted red as a background for the white skull & crossbones, and the rest of the airframe was covered in clear-doped fabric.
To further confuse the issue, Cole Palen had a replica
F.E.8 flying for a while. At first this was in an authentic standard finish of PC 10. Then, for some loony reason connected with his airshow routine (if I recall correctly), the aircraft was midified with a huge white skull painted on the nacelle with some sort of goofy cannon sticking out of the nose (later, this replica was turned over to the NASM and it was brought back to authentic form and the nacelle is there today, partially cutaway to provide an exhibit of a WWI aircraft cockpit, etc).
Perhaps your modeler took the DH 1A described above (or Palen's FE 8) and imaginatively applied it to some fictional DH 2 scheme.
Greg