Web 2.0 was all about networks and sharing. Heck, one of the biggest ideas at the time was "mashups". If-This-Then-That (IFTTT) got its start there. Yahoo! Pipes was a thing. Websites would freely provide RSS feeds you could not only subscribe to in your Reader but also use to create your own news feed in your dashboard that also showed you the latest issue of your favorite webcomic, the weather forecast and a stock ticker. Everything was beta. Most of it was free. Much of it could be fed into other things. Scraping was for hobbyists, not startups.
If anything, the walled gardens were Web 2.1. When companies realized that keeping data inside the platform rather than sharing it makes it easier to monetize.
I think if we're going with version numbers it also makes sense to describe the dot-com bubble as Web 1.0 as the biggest change that led to it was the massive increase in the number of people with Internet access making the Web commercially interesting (or viable). What some HNers fondly remember as the old Web is either the late pre-Web 2.0 days with webrings, Geocities and personal hobby websites (the latter eventually being supplanted by blogs, tumblr, livejournal and so on) or the pre-Web 1.0 days when most websites were hyperspecific hobby projects written by technophiles and hosted on Internet connected potatos or their university's web server.