I apologize for this terribly long and tl;dr post but it has some substance (I believe) in determining the kind of perpetrator they should be looking for.
You know, considering what information we were given initially, before LE imposed a dummy up order on Family, witnesses and medical staff, we know that
A. Someone witnessed a person on fire walking down the road.
B. Jessica had accelerant introduced orally/nasally or both.
c. Jessica gave a name or names to first responders.
All of those can be somewhat corroborated through evidence or statements.
A. The soles of her feet weren't burned but every other part of her body was "seriously" I would imagine by seriously that would indicate a burn beyond first degree. That could mean she was on her feet for a time. Even if she had very durable soles, the uppers on her shoes were likely obliterated as she had serious burns on her dorsals.
B. I'm not sure how exactly anyone other than a medical professional could make that particular evaluation, but Ali Alsanai corroborated it by saying LE provided that information to him, and Ben Chambers later did the same quoting medical personel.
C. It's been reported too many times by too many sources to reject it as hearsay in mnsho. I've even read somewhere that she was screaming in the hospital, soandso did this. Now before you go poohpoohing the possibility, talk to people in burn wards. People that can tell you how long before the swelling, blistering,and inflammation which accompany serious burns would prohibit speech. I know damned well if someone set me on fire, I'd struggle with my last breath to damn their *advertiser censored* to prison.
I have a point, I promise.
I believe fire was the murder weapon and it was intentional although I myself have one possible counter argument for the theory.
A beating gone too far, and fire to eradicate the evidence. Okay, that assumes two things. The perpetrator(s) believed Jessica was dead or near death. Although initially we have reports of a gash to the head, Ben Chambers now vehemently denies it. The sclera should exhibit the presence of blood in serious head trauma, and no report seems to mention any form of assault. If so why didn't LE offer, they beat the hell out of her then set her on fire to AA? I think much of this theory is attributed to Ms. Wilkerson's observation of they went too far. Well yeah, setting someone on fire is too far, but it doesn't have to imply an assault beforehand. Here is where my counter argument comes in. If by chance you set someone on fire, and they woke up as people ablaze tend to do, you might very well haul *advertiser censored* out of there when they emerge screaming from the vehicle. You might at that point drop the phone you were holding and determine too late you had done so.
Now on to my point. If you've determined fire is how you want to murder someone, you're a special kind of person. The kind of person prepared not only to cause suffering, but to observe it. You could change your mind midstream, but if you had that kind of conscience, you'd have already turned yourself in. Whoever did it, sat there and watched at least for a while. To be able to sit through that level of suffering is pyschopathic in nature, not sociopathic. Whoever started the fire did so when they knew Jessica was alive, even if just clinging to life. If she were so close to death from a beating, would she have lingered so long with thermal injuries so bad? Thermal injury was the cause of death, not organ failure, not a brain bleed, not cardiac arrest (although she certainly did suffer at least one)
My best friend was a grenadier during the Vietnam war. He frequently carried phosphorus grenades. Those are used as an effective demoralizing weapon. They burn the victim badly. and burn until the fuel is depleted. My friend told me "Joe, I still remember their screams when I hit a target(s) I will never forget them." He had people actively trying to kill him, and what he remembered was their suffering. Someone out there has forgotten, at least one someone, or they just don't care, because Jessica was less than human, to him, her, or them.
An enraged partner of an adulterous spouse? To set fire to a live human being? One of the first charecteristics of a true psychopath is the inability to cultivate and maintain relationships. I could see a jealous wife stabbing, shooting or choking a mistress without reservation, but burning her alive? Jessica died of thermal injury, not blunt force trauma, not asphyxiation, not blood loss, not complications from any of the above.
To hide the evidence of rape, or any evidence for that matter? The car was a complete burnout in my opinion. Jessica was there for at least 20 minutes. I'd say if they wanted to eradicate evidence they stayed behind at least long enough to see her exit the car, and would have at least crushed her skull with a boot if nothing else. She was left to languish as punishment.
You're looking for a person, or people who have a complete disconnect with humanity as a whole. Not sociopathic misfits. Someone who is so far removed from humanity they could sit and listen to that child screaming for mercy, and having no ears to hear it, or heart to feel it.
This wasn't an angry spouse, it wasn't a jealous boyfriend, It wasn't someone just trying to eradicate evidence. It was someone so disconnected from humanity that we can't understand their motivation. This wasn't an impulse crime, the few things we "know" don't corroborate with an impulse crime.
tl;dr synopsis, I believe that a psychopath or multiple psychopaths murdered Jessica based on preliminary reports. Reports provided before LE issued dummy up orders to preserve exposure on details of the crime.