I wouldn't worry about it. From what I can piece together from my readings here, this is a common practice. So, in other words, in future years, I would imagine that the absence of the tag wouldn't be a surprise (concern?) to serious collectors.
I for sure wouldn't walk away from the watch because of it. It's one of my absolute favorites in my collection, regardless of what name is written on the dial.
EDIT: Just saw you picked it up. Huge congrats!