Several people in the series intimate that they believe Burnham is to blame for the war and there are various things which might lead them to think so given that even she does not know why she did what she did.
1. She killed the original torchbearer which people may see as a provocation, there is no recording of this action and so no proof that the Klingon attacked first or if there was any reason why he should be killed at all. It could be possible that people believe that she was the aggressor and attacked as a personal retaliation for the death of her parents.
2. She distracted her Captain and Crew at a critical juncture, so people might feel that if she had not mutinied and incapacitated her captain then things may have been different.
3. After claiming that killing T'Kuvma would create a martyr and that the war would then become a holy war she then proceeds to kill him instead of stunning him after he kills the Captain.
4. She pleads guilty and fails to explain her actions in any way, her comments at the Courts Martial simply say she had high hopes and she has now lost them. It is about how she feels now not an explanation of why she did what she did.
5. Her reaction to the inference that the war is her fault from others does not raise a word of denial from her.
It may be one or all of these that lead the public and others in Starfleet to indicate that they apportion blame on her. We as the audience have a privileged view of the situation as we have been a fly on the wall throughout, something no other person depicted has.
So is she responsible?