I was there too, and that is not what I saw.
(Caveat: I'm thinking of the 1997-2000 period. Netscape IPOed in mid 1995, the bust was early 2000, so that covers the last 2/3rds of the first wave, but not all of it.)
My observations at the time: dotcom-1.0 was split pretty evenly between SF and SV, but there were clear differences in focus. Hardware and legacy stuff was all in SV, software/web/media was substantially all in SF.
Dotcom-2.0 (social media/SaaS/etc) was entirely in SF.
I'd agree that SF owned 2.0 and shared 1.0, but 1.0 in the city was extremely busy with founders, employees, launches, leases, and money.
I worked up and down the peninsula. Investors and data centers (VCs and DCs) were down south -- the latter with one exception: 200 Paul Ave, although itself at the extreme southern edge of SF.
Founders, staff, offices, and everything else were in the city.
I worked at one company who opened an office in the valley, but we literally couldn't hire people down there (Santa Clara), and couldn't get people to move there. All the action was in SF, for a software/web/media business.