The DC-X program, and others like it were spawned by private industry who were betting on a huge 'single stage to orbit' (or SSTO) model for satellite launches that would be needed for the Reagan 'Star Wars' missile defense program. They died when Star Wars died and NASA briefly assumed control of DC-X when its private backers pulled out but was stretched too thin to give it any real push.
That said, Elon and others will tell you that the current crop of rockets would not be possible without the work that NASA did and has shared. SpaceX also has benefited from computer systems that are 10,000X more powerful than the ones that NASA had available for their use, and materials that are 1/3 to 1/2 the weight and yet stronger than their NASA counterparts. Sensors that are 100x more sensitive and 1/1000th the cost. A six degree of freedom inertial unit was $125,000 in 1970 and resolved differences of .1G. A 9 degree of freedom unit from Sparkfun Electronics [1] is now $125, and reliably resolves 1/4096'th of a G. So I don't doubt that the same engineers at NASA could build what SpaceX is building today, today, but I assure you they didn't have the tools to build it back in the 70's or even in the 90's.
