Andy, I'll type slowly so you can keep up.......
The aircraft were @ 1nm apart. A 737 on descent at FL180 travels at @ 5nm per minute. That is 20 seconds apart . The RA is generated when the aircraft are 20 seconds apart .
Is there anything you are having trouble with so far?
They may have missed, had there been no intervention. The regulators aren't happy with that, hence TCAS was required equipment on the 737. "Might have missed" is not good enough, it seems, whenever it suits the regulator. Some on this forum are concerned about just where that line in the sand should be for "might miss".
To my mind, this incident is really effin embarrassing if you are pushing the NAS barrow.