b) This is exactly the kind of urban legend which tends to proliferate in human society, a cute lie which sounds believable. Like prostitution being the oldest profession, and the great wall of China being the only human made structure visible from space.

The story of the Internet is that it was developed in the mid to late 1960s by a couple of Universities in America and used by the US military to share resources across mainframes in each institution, as well as across institutions. Since then them main driver of innovation has been among universities and telecommunication companies finding optimal ways to deliver packages across telephone cables, antenna, satellites, etc.

The story of the Web is that it was developed in 1989-1991 to organize and link documents at the CERN research laboratory in Switzerland. Since then the main driver for innovations has been browser vendors competing and collaborating in developing browser technologies such that users pick their browser over the competition.

I don‘t know the story of online payment systems, but I bet the main drivers were companies opining up stores on the web and looking to replace pay by wire schemes over the telephone, and a bunch of start-ups who were able to find that market niche, developed software and sold it to those stores. The main driver of innovation here being start-ups. Porn sites and Gambling sites were no more important to that story as any other stores who sold art, golf-clubs, flight tickets, or hotel bookings.