You can with Github as well. And make changes to it via the website. Not on mobile though, unless you switch to the desktop site.

But you can't make changes to it online.

Depends. You're right if you use a conventional version control approach where you write on your local machine and then push to the server. But that's not the only way to use Fossil to store your notes.

If you're using the wiki (using one or more wiki pages) everything is entered into the browser whether online or using the built-in server running locally. Other options are to create an issue for each note or create a new forum thread for each note. The nice thing about these options is that you get the search and querying power of an sqlite database applied to your notes for free.

Disclaimer: I haven't used this approach because I don't use mobile devices for note taking. Just pointing out that it is possible.