Three of the four are fairly large regions ... For Thailand, though:
The short (and useless) andswer is: Yes, free camping is permitted in Thailand.
The longer answer is: Where, what's your idea of camping, and whose permission?
If you're not too hung up on official permission, then most places you'd want to camp are fine: you won't be bothering anyone and will likely not be bothered. Some of the larger/more popular national parks charge an entrance fee (which, gratingly, is higher for foreigners), and some of them have an official closing time. Most of them contain villages and often guesthouses/accomodation, so the idea of 'closing time' is a little hard to grasp.
To give you specifics: Doi Inthanon NP (Chiang Mai province) charges an entrance fee and has a closing time. It also has designated campsites, and 'structural accomodations' of varying types (proper guesthouses and bungalows or guided-trekking-related facilities). You could definitely get away with some kind of camping for free - after the entrance fee and against the (unenforced) rules. So that's a "soft no".
The NPs in Mae Hong Son province (actually like most NPs, especially in smaller non-southern provinces) are free to enter. They have designated campsites, a few of which I can verify are free.
If your idea of camping is like mine, no one will stop you from setting up a tent in a non-designated, jungley/forrested area; if you run into a ranger, he'll probably be curious why you'd do such a thing, rather than use the nice flat area (usually) near the park entrance - but he won't stop you.
As I said, there are villages in the NPs (in the north, these are mainly "hill tribes"). In remote enough areas, you can generally set up a tent near a village and be fine (and not make much fuss). In some villages, you might be invited to stay in someone's home; it would be nice to have a gift if you do this (a small amount of money or snacks and liquor usually go over well).
... So that's an 'enthusiastic yes - in many, but not all, places'.