The US government even ordered Lockheed to cease work on their jet engine and concentrate on piston engines:
"Lockheed had tried to produce a turbojet in 1940. Research engineer Nathan Price designed the startlingly advanced L-1000 with two-spool axial compressors aimed at a p.r. of 17 plus an afterburner, but when President Robert E. Gross took the brochures for the L-1000 and the L-133 canard fighter to be powered by it to Wright Field in 1942 he was told 'Forget it, keep building P-38s'."
"The Development of Jet and Turbine Aero Engines", Gunston, pg. 143
The DC-3, privately developed, was foundational for Army Air transport in WW2. The 707 was also entirely privately developed, and was foundational for all jet transport since. The Supermarine Spitfire of WW2 came from technology developed for Schneider Trophy races in the 1930's.
internet - the first internet was the telegraphy network, privately developed.
www - is not the first internet. BIX, Prodigy, CompuServe, MCIMail, RBBS, Timenet, etc.
It's not obvious that this was the wrong answer. The Germans were the first to field a combat jet aircraft, but it didn't help them much. The U.S. didn't really need the help, by 1942 it was already producing twice as many aircraft as Germany and Japan combined.
I think the real answer is "it's complicated." The jet revolution was not a single point event, and both government and private industry played a role.