I have to say, if you have a fallen saint, summoning dragons to terrorize the countryside, and a legend were to spontaneously manifest to counter it, I'd naturally assume it'd be the saint known for defending people from dragons terrorizing the countryside.
So here's one of the confusing parts of the "Heroic Servant" idea.
They are empowered by their legend.
In some cases, the legend alone can create people that never existed.
The legend is for the Saint Jeanne d'Arc.
How does Jeanne Alter have any power at all?
She has no legend.
It also applies to all the "true versions" of the Heroes.
It doesn't matter if the stories are wrong and the Hero is "real," since their status comes from the stories.
I am far from an expert but here is my opinion.
Jeanne's Legend started not from the moment she was a Saint, because that was awarded postmortum, but the moment a village girl decided that God needed her to save France.
From what little I've learned, Jeanne was an badass commander with a penchant for pulling off insane ideas to win, had zero fucks to give in most situations, and was a zealot that inspired those around her.
My headcanon is that the Ruler Class is stifling her true personality and bringing forth instead the ideal of a maiden saint, with gentle words and calm demeanor. Her purest incarnation would then be a Berserker with low levels (or EX?) of Madness Enhancement, with plenty of saintly and martial powers. But I digress.
Jeanne Alter's personality did not come from nowhere, and yet her Spirit Origin was designed to be a complete parallel of Jeanne's.
Her legend begins after Jeanne d'Arc burns for witchcraft, the 'end' of her legend, and her sole purpose is to erase Jeanne's legacy, France. And she works her way from the end to the beginning.
Gilles even comments on why he gave Jean power over dragons, to work off the legend of Saint Martha and the Tarrasque, but the truth is that Jeanne Alter was an unstable existance, meant to burn hard and crumble to ash. Gilles hooked her up to a grail, gave her power that keeps her existence stable, and gave her a goal to destroy all Jeanne OG loved and protected.
Jeanne Alter only becomes a 'true' heroic spirit after she dies ironically, becoming an Avenger that serves as the parallel Jeanne d'Arc with much in common and yet a mockery of each other.
To summarize, Jalter is an Alter, a reflection made manifest of a heroic spirit's dark thoughts that they would rather not face or embrace, and draws existence from that. That, along with the Spirit Origin of an Avenger, allows her to continue as 'a Jeanne that let grudges overtake her'.