In regards to Ontario Provincial Parks, during a fire ban twig stoves are not allowed.
The last time I looked into this it included a call to the Park Superintendent (Algonquin) and it was explained to me that an open flame needed to be controlled by a valve enabling one to instantly shut off the supply of fuel.
I assume that this also applies to crown land but can not speak for areas outside of Ontario.
On a side note, a few years ago following a 7 day solo Bev met up with me and we spent the next couple of nights in a developed campground. The first night as I was preparing to cook dinner, twig stove set up and the necessary pile of twigs ready to go we were visited by the local Park Warden and whens he saw the pile of twigs she was not happy.
Long story short, I barely escaped a fine for collecting wood from the local area by agreeing to toss the collected wood back into the surrounding bush. She went so far as to make me scatter what I had collected. According to her, I was soposed to purchase wood from the Park Office and whittle it down to something use able. Let's just say it was a good thing I had a liquid fuel stove with us.
Cheers
Rob from Barrie