What I'm reacting to is the discrepancy between "inevitable collision" and your experience.
I think it is not clear how "inevitable collision" is defined. The Tesla blog says
Automatic Emergency Braking, which will engage in the event of an unavoidable collision in order to reduce risk of impact
That does already not really make sense, because if a collision is unavoidable, risk of impact is 100%.
As you who had the system kick in didn´t crash, the collision was obviously avoidable.
I would say it reacts either in cases when there would be a colllision
A if driver does not brake
or
B even if driver would brake, reaction time would be too slow
I think the system assumes an unexperienced driver to make sure nothing happens, that is somewhere in between A and B. So to an experienced driver that might seem like, "man, why did he emergency break, I could have handled that no problem..."