I couldn't find the article yet. But I called the local fire department in my area and spoke to the head inspector that the sent the call to. He said that definitely the fire popping could have ignited your tree, with your screen open , depending on how dry the wood was, that 8 feet would not have been at all hard to have started the fire.
He suggested that you talk to the fire inspector, that inspected the fire at your place and they in turn can testify to this fact. They will have a report that should already be done to prove how and why the fire started, and how far a spark could fly to the tree.
I believe since their inspector said its only his "guess" that they don't have absolute proof on how far it could have sparked. Which means that it could have, and they can not refuse to settle your case, they are hoping you will take what they offer you, instead of what you deserve and what it will take to rebuild.
I hope this settles the question for you. Good Luck !
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