An application of diesel fuel kills not only poison ivy but all other vegetation in the area. Poison ivy roots extend beyond the leaf cover and the plant is likely to recolonise.
Tests in Alaska show that diesel oil spills kill all vegetation in the treated zone for more than a year. Nitrogen imbalances in contaminated soils prevent the quick return of anything but legumes.
The poison ivy you see covers the centre of the area the ivy has colonised. Runner roots creep out from established plants, allowing new growth from roots in clean soil.
Herbicides like Roundup destroy an enzyme plants need to live--all parts are affected, including roots. The herbicide must be absorbed through leaves and is not persistent in soil.
Diesel is used as a sticking agent for herbicides that prevent tree stumps from regrowing. The chemicals should be applied to the stumps and not to surrounding soil and vegetation.
In a diesel spill the oil leaches deep into the soil where natural processes do not break it down. Poisoning of the local water supply by diesel contamination is a real possibility.