From Wikipedia: The Rocketdyne division of North American Aviation was awarded the engine contract, AC Spark Plug the primary inertial guidance system, Bell Labs the backup radio guidance system, and General Electric the nose cone/reentry vehicle.

Douglas only won the contract to do the airframe and integration. It looks like a typical arrangement of the era. It’s not as if competitive bids have never been part of this process, they very often have. That’s not the point at all.