Almost correct. You do go to that server, but you don't need the server's admin's perms or anything.
View attachment 10547
Just click Follow on the feed channel,
View attachment 10549
Then pick a server that you have admin perms to add feeds in, and pick the channel you want the feed to appear in.
Then voila, it'll relay the same info on the server channel you picked.
You can do the same thing with other kinds of feeds that has the Follow button available. That's how I can have my personal server relay announcements from various servers I wanna follow the news of, like Srb2Dude's.