There is another issue here that does not appear to have been considered; that is the moisture content of the soil at the time of compaction and its relationship to the M/C at max dry density for either std or modified Proctor Compaction. For low moisture content soils, particularly those dry of the optimum m/c or below the m/c at max dry density, dropping below 90% of the max dry density may result in unacceptable settlement and or "collapse" on wetting up. I suggest you check out the ASCE Geotech Journal Vol 118, No.9 1992, pp1376-1395, "Review of Wetting-Induced Collapse in Compacted Soil" by Evert, Lawton, Richard, Fragaszy and Hetherington. The paper includes some good references from experience in South Africa as well as the US.
In my experience in typically clay soils in NZ where the soils are generally wet of OMC, using modified proctor as a means of compaction control means burning a lot of diesel drying soil out then compacting it to achieve very little additional benefit. So std compaction is generally used as the reference, except where low plasticity silts or granular materials are compacted. Then modified or "Heavy Compaction" is the std. Given the energy req'd to achieve modified Proctor is more than 4 times that used to achieve std compaction there is usually a significant cost penalty involved in using Heavy Compaction + the risk of setting up unacceptable construction induced pore pressures if the soils are wet of OMC. The relationship between air voids and density also needs to be considered. If water needs to be added to reduce teh energy req'd to ensure air voids at std compaction are say always less than 10%, and water is not freely available or is expensive, or the material will rapidly loose strength with the addition of water then reducing the air vodis through the application of "Heavy Compaction" may be the best option.
It is rare that there is not an area somewhere within a fill that does not entirely meet the specification but has passed undetected. The whole point of testing isthat it is a random statistically based approach to get to 95% or 99% compliance or whatever you chose to try and enforce. Testing is genearlly carried out to confirm a std higher than required if all fill is unconditionally guaranted to meet a specification to allow for "the one that got away", for variations in soil properties, and post compaction performance under cyclic and or slow increases in moisture content. The spec should match the post compaction long term load deformation criteria necessary for its intended end use.