It looks to be of a character that was created in Champions Online.
I would be really surprised. The Templars could retreat. They just couldn't convert to Islam if captured. Besides, what if you were ambushed?
Back armor is heavy though, if you are ambushed you circle up. Breastplates are risky, but the mobility improvemnt is a big positive.
If you have giant wings coming out of your back, putting on a back plate might be really difficult and restrict your flight. Especially if you put your armor on yourself and don't have a squire or something to help you.
Right, we get that - the question is just why the templar armor was designed to be wearable without the back, since the templars in question probably didn't have wings (OR DID THEY DUH DUH DUH!?).
To be honest, I don't think I've ever heard of people actually wearing armour that protected the front and not the back. It seems like it would be unbalancing. Besides, plate armour was worn over other armour, anyway, because without a proper under-layer, it doesn't provide protection.
I know vanishingly little about ancient armor, but didn't at least some breastplates cover only the front of the torso and not the rear (or the arms)?
For what it's worth: I majored in medieval literature and minored in history (focusing on the Crusades) in undergraduate, which included a 25 page historiography on the roles of women in the Crusades. I've done more reading in Crusades-era chronicles than anyone really should.
This is the first I've ever heard of any medieval-era warrior having backless armor. Considering that most of these knights were actually wearing chainmail (rather than the much more expensive and much later-developed plate), backless armor was simply not something used by any Templar worth their salt.
If you go back to Rome a Breastplate had a front and a back. As swords got better though the breastplate fell out of favor and Chainmail largely replaced it. The Templars of history would have mostly worn chainmail, as plate was worse armor than chain at that time. They also didn't do the big crosses like we see on Fanatic's Armor, they did small ones generally on the sides, and the helmet like she wears on her Reedemer card is also non-templar era.
The Templars disbanded before the Plate breastplate returned to fashion, and when it returned it was mostly a front piece, unless you were a wealthy Knight with a big war horse, then you wore full plate so you were largely unkillable and could ransom yourself if captured. The rest wore a front plate with a leather back, you weren't on a horse and had to pick your armor with that in mind.
The Breastplate persisted through the Spanish Empire in this fashion, as they even gave some protection against shots from a musket.
The design of Fanatic's Templar armor is frankly not in any way historical. The strapping on the Aegis of resurrection looks like a 15th/16th century breastplate, long after the Templars were gone.
If Fanatic was wearing Templar armor it would be a suit of chainmail.
This leads us to one of several possible conclusions:
1. While the >G guys strived tirelessly for historical accuracy, they sadly fell short in this instance.
2. The game was drawn to look cool and play more off of the mythology of the Knights Templar than actual History.
3. Fanatic is crazy. She forged the sword and armor herself, but believes she has been selected for some holy quest.
I'm leaning towards 2, but I'm not giving up on 3.
4. It is set in a fictional universe that has some parallels with the real world, but not every detail is exactly the same as our own.
I'd roll that under the play off mythology without looking at actual history.
Don't get me wrong--I'm okay with the armor design. It's just clear that it's comics-armor, not historically accurate. Doesn't bother me. :D
Maybe that was the ceremonial armor of choice of the Peruvian Templars...
Is it just me, or does the word "Peruvian" nowadays conjure up images of gigantic deadly guine pigs?
/shrug
I understand your reference! 
Also, the Peruvian is a breed of long-haired guinea pig (I used to breed them).
I never knew that. Learn something new every day
The first thing that came to mind was the infamous "Peruvian Puff Pepper". Haha.