okay, technically it was the capitals fault by extension because they are the ones that make people work in the mines. although it isn't their fault because they don't want people who provide for them to die.

There is no way to prove that it's the capitol's fault for Katniss's dad's death. something may have just gone wrong in the mines by accident. but it's also possible Pres. Snow could have set it up to kill someone who was causing trouble, Katniss did mention how easy it was to make anything look like an accident down in the mines.

Well on the whole I guess it is because supplying for the Capitol was the whole reason Katniss' father, and the rest of the miners, were down there. I suppose there's no way of knowing whether it was purposefully on President Snow's part for some reason or not, but there was always gonna be that risk anyway.