No, its not true at all, the british army uses diesel in all it's vehicles and has even developed a diesel motorbike.
Being a member of NATO which has chosen the 9mm bullet as the standard, most nato guns will fire a 9mm round, so in a war situation or in a difficult supply situation ammo can be interchangeable amongst NATO forces.
They also has a "single fuel policy" which is that all vehicles run on diesel, and the diesel vehicles can also run on avgas (jet fuel), again this makes life easier when resources are stretched or when supply lines are erratic.
Diesel has the added benefit of being less flammable and more does not expand like petrol.
Hope that helps