Of course he was using the Internet. Stallman receives/sends *many* emails,
what requires the Internet. You are actually talking about browsing the Web.
Here is how he accesses the Web:
I generally do not connect to web sites from my own machine, aside from a few
sites I have some special relationship with. I usually fetch web pages from
other sites by sending mail to a program (see
git://git.gnu.org/womb/hacks.git) that fetches them, much like wget, and then
mails them back to me. Then I look at them using a web browser, unless it is
easy to see the text in the HTML page directly. I usually try lynx first,
then a graphical browser if the page needs it (using konqueror, which won't
fetch from other sites in such a situation).
I occasionally also browse unrelated sites using IceCat via Tor. Except for
rare cases, I do not identify myself to them. I think that is enough to
prevent my browsing from being connected with me. IceCat blocks tracking tags
and most fingerprinting methods.
https://stallman.org/stallman-computing.html