The original article (https://news.ycombinator.com/item?id=33127459) doesn't mention batteries either, but it would make sense only to effectively put them in airplane mode. Hundreds of tags transmitting is bad for the same reason that phone's have to be shut off during flights. It even says "This is specifically because of the transmission function".
Again, this isn't about battery fires - which is why they are't specifying quartz watches or pocket calculators too, but AirTags.