That would be my first guess, since the top MOVES, the trunk sensor and the one in the frame over the passenger's head must be ok. It DOES sound like the sensor in the windshield frame is not "telling" the TCM that the top has been secured and locked, until it does, the system's cycle is not considered complete and the light stay on, violating the nine mph rule would cuase an alarm, putting the top down silences the alarm because the windshield sensor is not EXPECTED to close when the top is stowed away.

I would suggest they replace the sensor in the windshield frame and see what they get it to do. (I guess you could look in the manual and measure the voltage from that sensor at the module. I am at work, can't remember if that sensor is wired to the Body Control Module or the Top Control Module.)

WAIT A MINUTE:
Maybe check to see that the hooks are working right to "grab" the sensor, I remember the sensor being in the passenger side hole in the frame, you can use a skinny finger or screwdriver and "work" the sensor by hand. Mabye a screw or something is in there keeping it from moving? Maybe the whole latch assembly isn't REALLY fixed right and therefore not pushing the switch closed?

Kinda sounds mechanical to me - switch may be ok, but maybe the latch stuff isn't pushing on it right.