I've no experience with Tag (or Omega) servicing in Switzerland but horror stories like these continue to reinforce my position on NEVER sending a watch to either of them for service.
It's unfortunate that they have literally a candy store of watch parts that any enthusiast would go crazy over if on site but they refuse to acknowledge the wishes of the owners hence why they will never get a penny of my money. It's a shame really, the only place with the proper parts (assuming they do somewhere in their treasure trove) can't seem to do their job properly (and that they won't sell parts to those that are competent.