Lithium Ion batteries do burn much more readily when fully charged than when discharged -- this is because they self-discharge rapidly at elevated temperatures, which provokes an even greater reaction of the materials inside of them. Specifically, if the cathode of NMC/NCA batteries gets hot enough, it will decompose into oxygen and really kick off the graphite + electrolye burning.
Discharged batteries are tougher to get to burn since it's harder to heat the cathode to that point externally so oxygen has to come from the environment.
