A hundred years ago, anarchists were shooting people from Milwaukee to St Petersburg. Marxism-Leninism literally took over multiple countries. As long as you have global movement and communications, you have global spread of ideology, you don't need the Internet.
As long as you have cows you will have hamburgers, indeed! But the availability of cheese can nonetheless change the frequency of hamburger, as well as their individual qualities.
By using the internet for radicalisations (a fact almost universal along recent attackers in the US) these people have quite clearly demonstrated their believe in the effectiveness of the net for their cause.
We usually rely on local, individual decision-making to optimise everything, and I don't see a reason why these people (despite their obvious moral failures) should be an exception from this dramatically successful concept. This evidence becomes even stronger considering we're looking at the subset of "successful" attackers.
It also feels intuitively correct to consider the net a tool that helps such movement. That's just because by default, it seems to help almost every endeavour in some way or other. Radicalising a young white nationalist isn't much different from getting them to vote or buy a specific brand of sneakers. If anything, the specific challenges of illegal activities of a small, geographically dispersed set of loners seem to be a unique fit to this particular tool.
Like your racist uncle, before people just heard him rant at the thanksgiving table but now the whole world can read his rants on Facebook. The racism was always there, it is just harder to ignore today.
So I'd like to see proof that the Internet actually helps radicalize people. It is true that it makes it easier to find radical groups, but it also makes it easier to find other views which would hinder radicalization. Before if you made a few radical friends they could easily become your whole world! So my naive assumption is that both forces roughly cancels each other out making an open Internet mostly neutral in terms of radicalization.