When I first read this, having been a p-chem nerd long ago, and having had some burns, I had questions about how one could get a chemical burn on one's arms from a relatively small battery in headphones. It turns out that lithium battery fires produce HF, which you do not want to be exposed to at all. Very plausible that HF and other chemicals in the fire could cause a burn on skin without splashing any liquid around. In fact if there was any concentration of HF large enough to be splashed, it would have been a potentially fatal risk. If I ever encounter a burning Li battery, getting it out of an enclosed space would be a high priority.