My Omega SMP was serviced last year by Omega. It has since had to go back TWICE for issues related to the overhaul...broken crown, non-functioning power reserve. When I posted this issue on another site, I was told by a number of people to avoid sending it to the New Jersey service center. They were said to be rude (yes, they were) and unreliable (yes, they were...mine was twice delayed). However, because this was being covered by warranty, it had to go back to NJ. On a positive note, it has run perfectly for the past 2 weeks, and it winds smoother than before. Hopefully, it will continue to run well, but if it doesn't, I'm going with someone local next time. I won't buy another Omega, however, not after this experience.
I also had a similar situation with a Tourneau in NYC, only it was they who lied and told me my IWC watch was sent to Switzerland for servicing, and it wasn't. Same thing happened with a Rolex AD, who sent my Submariner to their corporate service center after we agreed--and she wrote it on the work order--that it would go to the Rolex Service Center. This is why I won't have an AD send in a watch for me. I do it myself.
Best of luck with yours!