LEM,
You say: But somebody is of a different opinion...
Looks like trouble for you.
Two questions arise. I don't know the 737 - as I'm just an ATR driver, so:
First: What does the AFM say about any alarms on a CAT III approach and the subsequent procedure to apply?
(Does it maybe say something like - GO AROUND?)
Second: What does your companies operation manual or procedure manual say about "ANY" alarm on an armed CAT III approach?
Ours says: GO AROUND! Simply because you cannot tell the system implication within - lets say (300 ft) = 20 sec? !!!
error_401