Its hard to say what the issue was
..seeing something in person doesnt compare to seeing the jewelry in hand but I do feel like this is authentic. Its very unusual, almost unheard of, for Tiffany to do some sort of service the piece however, then send it back it you. As a general rule, Tiffany wont do anything, clean it or service it, if its not authentic.
It doesnt happen often but sometimes vintage pieces can be challenging when they are sent for service, especially if they have been modified. I ran into this myself two years ago. I had a very old, 1970s bracelet that I sent to New York for service. Ten years ago however, I had several of the jump rings replaced by a non Tiffany jeweler. The piece also had an accident and the area that had the hallmark signature was damaged. It was melted back into place but in doing so, it slightly distorted the markings. The bracelet sat in the New York service center 3 weeks before I got a call from a customer service rep telling me there was an issue with the authenticity. I asked for a manager explaining the issue and asked for a second opinion, preferably from a rep with experience in vintage jewelry. A week later, it was repaired without issue and sent back to me.
I agree that the techs should know and recognize Tiffany jewelry but I guess it all depends on the experience and knowledge of the tech who gets the piece to work on. If the pendant you have tests for true silver and has a real diamond then that leans towards an authentic piece. When the tech gets an older piece like this and they dont know its history, they need to go back into the achieves to verify that it is a Tiffany design. Since this item you have appears to have a loop on the back, maybe they were looking for a pendant. If this item was originally a brooch or pin (and I think it was. The T signature on this piece was used mainly in gentlemens jewelry) and they cant match it to an original Tiffany item, that could raise a flag. If you want to pursue the issue with Tiffany, I think its an issue worth pursuing with them.