^^^ Did you verify the serial number to make sure it matches the one originally given to you? Transcribed numbers can happen.
How did the Tokyo Omega shop verify it was 1997?
About the serial number, obviously. The serial number on the lug matches the one inside the case etched on the watch movement itself. But you don't need to know that number.
About how they identified it, I don't know. Because it's SWATCH. I don't have detailed answers on that, I don't work there. I took it to the NICOLAS G. HAYEK CENTER which is a 14 story building in Ginza owned by the SWATCH Group. A technician behind glass looked at it and identified it. Customers are not allowed to go back there, but I could see him working. A customer service rep was the in-between him and me disseminating the information he was giving her. Anyways, I believe him otherwise he wouldn't be there.
This. I am not convinced that it is as definitive as you think.
Listen guys, I have to be honest with you. I'm not going to entertain the conversation about the watch, and the date of the watch anymore. I kind of don't care whether you believe me or don't. I'm inquiring for help now about something specific, you can either help me try to find the box or don't, but I'm not going to keep going back-and-forth with anyone about my watch. I don't know you.