Log Shipping Backup and Destination Folder Location
Recommendations are accurate. Reason 1 being never keep you backups on your database server or disk. Just good practice to separate them in case of disaster. Ideally you want you backups on different hardware as well, or even different location/data center. Approach it this way, if disaster struck, would you be able to recover? if not, what was your point of failure, server, disk, infrastructure.

The scenario you reference to on MS page explains multiple copy and restore jobs to multiple secondary locations. Copying to each secondary and restore keeps unique history on the jobs for that instance. As MS states "The primary and secondary server instances send their own history and status to the monitor server instance."