I've always played Intimidating Authority as an Ability that you may use in step C, but whose effect is applied at step D. The difference is subtle, but it means, eg, that an Intimidating Authority model must determine whether to discard a card BEFORE an attacking model chooses whether to reduce the Focused condition to add a positive modifier. This application of the Ability's timing also means that Intimidating Authority models don't know whether the attacker will choose to reduce Focused, etc.
Flexible Morality has the same timing issue. There are a handful of others like Beer Goggles that aren't wholly clear, because they're Activated Abilities that are Activated in step C, but whose effect is in step D.
I imagine a lot of people intuitively play it Solkan's way, which doesn't affect anything else in a majority of cases. It's mostly when Take the Hit changes the target that you need to determine whether any of the effects should be generated in Step C, whether they carry over to new targets (Intimidating Authority, eg, places an effect on the Attacker, rather than being a matter of the Target being any particular thing, so it can theoretically carry over). Honestly, it's worth asking your local TO how they want you to play it.