GAO has a report on duplicative payments by USDA farm agencies. Basically, they found a lot of overlap (producers getting benefits from multiple programs) but not a whole lot of duplication (producers getting benefits from multiple programs for the identical cause, such as loss of production). They did recommend data matching in cases where duplication is possible, but RMA and FSA pushed back, arguing lack of resources.
Bottom line: even though the taxpayer would gain if they identified the duplication (because the cost would be less than the money to be refunded, assuming there was 100 percent collection) it doesn't make sense to managers. Assuming managers are good and rational, they see a bigger bang for the personnel and IR bucks in other areas. The answer is to allow the agencies to keep part of their collections, but that's not something likely to happen.