No, it is not true. You're misunderstanding how this works.

The document you link is using ssh as a transport protocol as opposed to the rsync protocol. The rsync binary must be installed on both systems for this to work.

When you run something like:

rsync file user@rhost:/dest/path

The local rsync binary invokes ssh, and then executes the rsync binary on the remote system and from there the two instances of rsync effectuate the transfer.

If you do not have rsync available in your path on the remote system you will not be able to copy files over ssh. This is documented in the manpage.

Try it.

Exactly. You absolutely must have the rsync binary installed locally. The rsync "server" should only actually be run if you know you need it (that is, only if you are providing rsync services to other people).

As others have pointed out, that doesn't quite work. But the way that I use rsync with my remarkable is to use sshfs to mount the remarkable's filesystem, and then run rsync between the local and mounted filesystems. Works for me without having to install rsync on the remarkable.

Unfortunately you will not get any speed boost in that case, in fact it will be slower having to fetch all the remote side data for small file changes.

Fair enough. It does work for my simple use case: rsync student coursework to the remarkable, mark coursework on the remarkable, rsync back. There aren't many small file changes and USB is fast enough. The real bottleneck is the marking but I'm not sure if I want a package manager to help me with that!

Doesn't that run rsync --server on the server via ssh?

yup.