The dealer is not incorrect.
The thermostat should only fit one way.
Since it overheated before you changed the thermostat, suspect obstruction and/or leak. The obstruction could be anywhere in the system but my guess -- which is entirely worthless -- would be the hoses or the rad itself.
Let the car go stone cold, start it, and wait to see if you have circulation. That will tell you the thermostat is opening without removing it again. If so, then suspect poor circulation. Burp anyway since you've opened the system, and see what happens.
Has there been a pressure test? If no, do it.