What if the note you are sharing is from a relay that is not common with the sender?
Discussion
common with the sender and receiver*
My point is the receiver won't see the DM at all if they don't have a common relay so it doesn't help to embed the relay address within the DM.
The relay you are using for the DM can be common but the note you are sharing can be on a relay the recipient doesn’t have. So they see the DM but don’t know where to fetch the note, which is what you described happened