I think we need to get away from the "natural" vs "artificial" distinction.  One big problem is that we literally don't have any characters (at least ones that have been accepted) that received their powers "naturally".  So, let's go through them, shall we?

Heroes
Arachne -  powers granted by formula
Bast - powers induced by magic
Cross - none (as far as I know)
Hydro - powers granted by accident with water
Icarus - powers granted from alien tech/symbiotic relationship
Icon - alien / human hybrid
Iron Knight - none / power suit
Lyger - powers granted by blood transfusion with metagene
The Mage - magic powers
Myth - powers granted from magical weapon
Pendragon - none / supernatural weapons
Raptor - powers granted by formula
Riley - alien / human hybrid
Sigil - alien
Theodore Roosevelt - none
Thunderbolt and Boom - "miracle"
Wasp - powers granted by formula
The Wolf - magic powers

Walking the Line
DeathDealer - none
[b]Equilibrium - maybe naturally born ability[/b]
Hecate - supernatural character
Polemos - enhanced by "super soldier" formula
Racheli - alien symbiotic relationship
[b]Silence - maybe naturally born ability[/b]
War-Pulse - abilities granted by scientific project
White Witch - magic powers


Villains 
The Cowl - none (as far as I know)
The Forsaken - genetically altered
Lord Khonsu - "god"-granted abilities
[b]The Red Reaper - inherited metahuman status[/b]
Umbraxis - Alien

From the list in the OP, there are three characters that probably would be considered having "natural" abilities.  However, even being born with the powers can be problematic.  Spider-Man, according to your guys' definition, would be a metahuman because his powers were not "natural".  However, would you consider his daughter (either Mayday in MC2 or Anna in Renew Your Vows) a mutant or a metahuman (or mutate in Marvel terminology)?  Mayday/Anna were born with their powers, bu they inherited their powers from their father, who did not receive his powers naturally.  So would she be a mutant or a metahuman?

This line of thinking could even be taken further.  So, mutants are supposed to be created by evolution.  But what if the first mutants were really just humans that have been altered by either aliens (as the mainstream Marvel mutants are) or by other humans (as the Ultimate Universe mutants were).  This even expands to the Inhumans, who were experiments by the Kree.  Where is the line drawn?  Sure, after several generations, the powers would be "natural" because nothing beyond dominant genes would cause them, but that gene was created artificially to begin with.

Therefore, I think that a better schema would be the source of the powers.  Are they hybrids?  Are the powers the result of a gene(s)?  Are the powers magically induced?