That's true, but what matter for technology development is who is specifying the design criteria. For most of the history of US rocket development it's been NASA. They designed the Saturn V, the Shuttle, SLS, and sub-contracted out manufacturing to private industry. The contractors certainly had a lot of input into the detailed design of the rockets, but the overall criteria and design concept were defined by NASA.

With COTS NASA switched to contracting out for launch capacity without defining how it must be achieved. This allowed SpaceX the freedom to engineer their rockets as they saw fit.