Death Caller: Clarification

How does Death Caller interact with effects that destroy a target if they're brought below a certain HP threshold?

Death-Caller

Title

After a target destroys a target without dealing damage to it, put this card under the surviving target, covering everything above this line:
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Whenever this target reduces another target to 3 or fewer HP, destroy that target.

The effecrts I'm thinking of are KNYFE's Flawless Execution, Fixer's Tyre Iron or the Sentinels' Fling Into Darkness.

I can see a few ways of the power working.

1) If you've ever done damage to that target, you can't gain it. Book-keeping nightmare and silly. Included for completeness.

2) You damaged them to get the destroy effect to activate, so doesn't count.

3) Flawless Execution and Tyre Iron work as the damage is a separate thing, but Fling Into Darkness wouldn't.

4) You did not directly destroy the target with damage, i.e. HP were not reduced to 0 or less, so they all count.

Personally, I think 4 is correct, with 2 being an alternative interpretation. 3 is possible but seems needlessly fiddly and restrictive and 1 is obviously silly.

Thoughts from the community?

As an aside, Captain Cosmic is ripe for this one with all his construct destruction effects. Or, indeed, almost anyone if you have Imbued Vitality out.

If the target is removed from play by an effect that doesn't deal damage, then they would get the title.

Sucker Punch, Wrathful Gaze, etc.

Fling into Darkness works exactly like Tyre Iron and Flawless Execution do. The damage and destruction are separate events in all these cases.

All three are good for getting that title. In this game nothing happens simultaneously and everything that happens is its own discrete event. So you Fling a target, bring it to 4 HP or less, this triggers the rider on FiD and the target is destroyed without taking damage.

Now the real question is: who among the Sentinels gets the title? I'd say a Sentinel of your choice by rules, beause there's no indication the Writhe character did the destruction (other than fluff)

Another instance of poor wording: all cards that destroy a target say "[you] destroy a target". There's no indication that it's a target doing the destruction. Of course rule of common sense helps...

That is a really good question.  The wording makes me think it could be #2.

However, in playtesting it was generally used as #4, and no comment was ever made about it, so I would assume the intent is #4.

I was #4, but now am leaning toward #2 due to Christopher's ruling hinting that Titles look back at the turn.