Consider this scenario: The 18F team works with the Secretary of the Interior's office to draft requirements for a system needed by the Department of the Interior. They gather the requirements and conclude "This isn't a huge system. We can do this ourselves." Do the individuals working at 18F get raises or massive bonuses for doing the work, or do they continue to receive the same civil service graded salary they've always been receiving? It is certainly in the 18F department's interest to have work and continue to exist, but I don't see any huge payoff to the head of 18F the way there would be if a large company got a contract.
Or, to sort of repeat a scenario I offered earlier in this conversation, my wife wants our bathroom remodeled. I interview her and find out what she wants and write it all down. I go over it with a few companies that do bathroom remodeling. I receive their bids. I conclude that I'm capable of doing the work myself more quickly and more cheaply. I award the "contract" to myself. Where's the conflict of interest?