boy, that sounds like a mess. contractors always have a high number and owners always have a low number. for the site, if you take the total acres minus the pad area, then multiply by the depth, that should give you the in-place neat quantity. however, when you dig it out it will take up more room in the truck (because it fluffs up) but when you put it back in, it should shrink due to compaction. if it happens to be rock that you take out, the quantity should swell since you'll never get it as tight as it was originally. there's many different ways to look at the scenario...does removing well compacted fill swell more or less than residual soil when you dig it out.
to answer your question, it all depends on how the specs are written and how the contractor gets paid. i always ask for how everyone figures their numbers. that way you can see where the differences are. if they say they used a computer program, i would be suspect of them. i've seen that almost cost the owner 22,000cy of mass rock on one particular shot of many (they forgot to account for the 20' cut which had already been made -- i.e. had 20' too much rock in the figures). get everyone to agrees on shrink/swell factors, areas, depths, etc...then it should be a matter of getting the math to work out...lock everyone in a room to fight it out...that usually works.