I think the reason for these rules is that burning this kind of material (including wet wood or other woodlike substances) is that they create a lot of toxic dioxines. These particles then drift down onto nearby plants, and of course you do not want to ingest these as dioxines are extremely carcenogenic.

In this case, the dioxines are produced by molds on the wood (and perhaps carton?). In Belgium a study showed that on certain days, 25% of dioxine pollution is caused by people burning garden waste.