Why does the NASA GL-10 Greased Lightning run on diesel?
There is a bit of a misnomer here, although the plane runs diesel engines it most likely does not run traditional diesel fuel as you would find at a gas station. Diesel engines can be run on Jet-A which is available far more widely than 100LL at airports outside the US which Ron mentions. 

There are even some applications for diesel engines in GA as noted in your linked question the diamond twin star and now the Piper Archer DX have successfully been running diesel engines for some time now. 

According to this paper the Cosworth AG engine was considered which the Navy has already been bench testing with JP-5 and JP-8 jet fuel. Presumably the GS motor they chose runs similarly.