Because it is wholly undefined. The only mechanic we have in 5e for Divine Intervention is solely in the cleric's domain. So, be default, the fighter in question can't. In 4e Divine Intervention is undefined as well, there isn't a mechanic for it.* So in 4e the fighter can't either. In AD&D the fighter could, and there is a defined mechanic. Unlikely, but possible.
pemerton gave us two examples of how he steps outside the given ruleset and allowed the action to occur.** It was an ad hoc ruling within the scope of the table's play. And that's fine. The rule set doesn't matter, it is a style of play.
So we circle back again to the question being in regard to style of play not rules of play. The answer to the original question is "Not Applicable - the character and skill are unable to achieve this goal." Could you allow this? Sure, make a rule that allows for such, and adjust the rule as necessary to prevent abuse. Should you allow this? That's for the individual table to decide.
Interestingly to me, the OP and the example are at odds with me. I was thinking of low level characters from the example, because higher level characters would have other options. But, that's me.
*There is a specific level 25 power Divine Intervention; you swap places with your buddy, take the hit, and explode doing lots of damage. Not applicable for our discussion.
** Which had nothing to do with the OP, except as, maybe, a "player-facing" mechanic.
What you're saying here is incorrect. In 4e, a Fighter player can:
* invoke divine intervention.
* it is entirely within the ruleset.
* they don't have to even invest in a multiclass feat for Healing Word to do so (although they can if they like).
1) Hit Points in 4e represent "resolve" among other things. They aren't meat points (nor have they ever been). We know that from dozens of sources. Further, the Religion Skill cites "soothing grief and panic" as but one example of an improvised use. That is "restoring resolve."
2) Religion is the keying skill for Rituals to employ this magic. This is important because (a) you don't have to have Divine keywords to "have the gods hear your pleas and answer them (with all sorts of benedictions and ceremony from the relatively mundane like purification to the sublime like demanding immediate audience and having questions answered with a cosmological power)" and (b) Religion is clearly the skill this keys off of. A Fighter can take Ritualist, pay the cost, make the check and they get the benefit.
3) A Fighter can also take any of the following Religion Skill Powers that do not have the Divine keyword yet clearly invoke divine intercession via
mundane (none of these are magic) pleas to gods/belief/hope in some kind of metaphysical aid
that are answered:
Faith Healing Religion Utility 2
Your prayers help an ally recover from injury.
Daily ✦ Healing
Standard Action Melee touch
Target: One creature
Effect: The target can spend a healing surge.
Deliverance of Faith Religion Utility 6
You give of yourself in the belief that somewhere, something will give a little back.
Encounter
Minor Action Personal
Effect: You spend a healing surge but regain no hit points. You gain temporary hit points equal to your healing surge value.
Conviction Religion Utility 10
You whisper a prayer for aid to overcome hardship.
Encounter
Minor Action Personal
Effect: You gain a +5 bonus to the next saving throw you make before the start of your next turn.
Recitation Religion Utility 10
You echo your allies' prayers to give them strength.
Daily ✦
Zone
Minor Action Close burst 1
Effect: The burst creates a zone that lasts until the end of your next turn. When you move, the zone moves with you, remaining centered on you. While within the zone, your allies gain a +1 power bonus to attack rolls.
Sustain Minor: The zone persists.
4) A Fighter can take a Character Theme, a Paragon Path, or an Epic Destiny that does the same as above (invokes religious themes with
answered prayers and healing/bulwarking but
without the Divine Keyword, so mundane prayer, therefore signifying that this character is not a de facto agent of divine sponsorship).
5) The game, at every opportunity, tells the GM to be permissive and gives them an extreme amount of guidance on how to resolve both in-combat stunts using specific skills (like Religion) via DCs/Damage Expressions/Tier-based effects/Costs for failed checks as well as how to resolve Skill Challenge action declarations (like praying for intercession through the use of Religion). Dungeon Magazine has actual examples of this usage in their adventures.
6) Actual DDI Dungeon Magazine adventures show tons of improvised uses of ceremony and invocation of faith/belief-infused prowess like the below:
Religion (Medium DC 16):
By performing the rites that were never received by those who suffered here, the character allows the restless spirits to gain a semblance of peace and end the hatred and fear that powers this place.
7) Terrain Powers and Traps/Hazards in the books explicitly call out the usage of Religion as Countermeasures/Triggering Skills (like so):
Lightning Pillar Strike At-Will Terrain
At your command, lightning lashes out from an ancient stone monolith.
Standard Action
Requirement: You must be within 5 squares of a lightning pillar.
Check: Arcana, Nature, or
Religion check (hard DC) to trigger the pillar's attack.
I don't know how many times I've constructed posts like these in the last 10 years when things like this come up.
No big deal. I'm sure you mean no harm, but you've just got this wrong and its an easy course correction. Please, for my sanity, just upload this information and whenever you see someone in the future making the above claim that you did ("to use Religion in such a way is to go outside of the ruleset/instruction for 4e"), please correct them. Feel free to C/P this post or just give your own abridge version of the correction above.
