Frankly, whether you had the Protective trait or not is irrelevant at that point imo. First of all, your crossbowmen is level is somewhere around 9, in a city that has walls (+50%) and a +20% culture defense, and on a hill. So for now, the multiplier is at +145% at that point for non-melee units, and +195% for melee units unmodified. Lets not forget that your crossbowmen are also lead by a Great General, which explains its high level. So examining the upgrades you gave it, that's another +20% on hills, +75% defending in cities, +6 first strikes, -60% to collateral damage, plus another +10% against melee and mounted units. That puts that one single unit's combat modifier against enemies at +240% against all non-melee/non-mounted units with six extra first strikes and -60% to collateral, and +300% against all melee units with 6 extra first strikes and -60% collateral, and +250% with all the aforementioned collateral and first strike bonuses against mounted.
Doing a little math, that would make the strength of your crossbowmen against most units 14.4 with 6 extra first strikes and -60% to collateral damage. Versus melee units, that strength gets boosted to 18, and against mounted it is 15. And I'm not even going to go into the possible extra +25% for digging into that city in the first place. Frankly, it wasn't you traits that saved you, but rather your science and great general. I could get the same conditions quite easily without the Protective trait.