scp and sftp make sense, but is that really the case for rsync?

As far as I remember, rsync does a few neat tricks like hashing files on both sides of a connection to determine whether it's worth transferring them over a potentially slow connection, which would not work with pure sftp.

You're correct, rsync operates over SSH (or its own native protocol) but runs a copy of the rsync binary on the remote side rather than using the SFTP subsystem.