I see this note in many relays.
Discussion
So people have been syncing stuff on the background.
There are tons of services running that reshare notes everywhere. They are the reason why nostr works.
Try writing to only stoner, worked for me ๐ซก 
Also, my understanding is that if I click โrebroadcastโ in my Nostr client, it will go to all of my relays regardless of the ones the original user had broadcast to, correct?
Correct
Not everywhere, no. I've been looking and haven't seen that type of widespread rebroadcasting. I think this is just between some small sets of relays, and only with some users perhaps? Otherwise Nostr would definitely not work at all.