What you say is absolutely true if contracts are never involved. However, almost any procurement ends with a contract between the service or commodity supplier and the government, which really becomes the main barrier to entry to OSS and makes those questions from before more sticklers than commercial flavors of doing business. In the commercial world, everything is fine and rosy with contracts, they are flexible and can be redefined easily. In the government world, not so much. USC Title 10, the FAR, among other regulations, policies, and laws define how the government may do business, and they don't always easily align with the answers to those above questions. When they do, GREAT! When they don't, well, its back to closed source whether it wants to or not, because it may pass those wickets easier.
Don't get me wrong, the government can benefit greatly from the OSS community, and i also personally believe it should consider more OSS when looking for solutions to its problems. It is just many of the public policies, laws, and regulations make it much harder to do that than John Q. Public.