They mention the toxin comes from the rhododendron flower. I remember camping in North Carolina once and one of the people I was with warned against burning anything from the rhododendron in the area, as supposedly the smoke would give you the runs.
I mostly thought they were joking, and I have no idea what specific type of rhododendron would be there (if any), but maybe there’s a glimmer of merit to it? Or maybe they were thinking of a different plant?
This was somewhere in the Blue Ridge Mountains, if I remember correctly.
You also don't want to burn poison ivy because the oil (urushiol) is not something you want in your lungs if you are reactive to it.
i believe ingestion is the primary concern, but the smoke can also lead to symptoms, yes.