Wrong. The initial thingie that we now call "the Internet" was built by grad students & professors, with zero government oversight. ARPA financed it, but they didn't do any of the actual work, nor did they look over our shoulders as we got on with it.
AT&T helped, by granting us license to use UNIX[tm], but I can assure you that Google, MS et ali had zero impact on what we have today. Virtually very site that you are likely to visit today is a Johnnie come lately in the great scheme of things.
 DARPA came later ...