The topmost comment in this comment thread starts with the fact that there are over a thousand studies on this already, no? Even if the whole effect isn't well understood, it seems like there is some science behind this.
One could argue that the research goes all the way back to Dr Frederick Cook aboard the Belgica during an Antarctic expedition I which they became trapped by the sea ice. The men suffered from multiple maladies, scurvy included, with one of the prescribed treatments being to stand nude near a blazing fire for an hour. If his notes are to be believed, the men saw some immediate changed in their overall health beyond simply getting warm. By some accounts, he became a bit of a fanatic about how much we humans need the sun, after that.
Or it could be vitamin D, or sunlight killing ticks, or fungal pathogens, or it could be the release of endorphins due to mild sun burn, or any number of other things.
I'd say it's all those things, likely in different combinations based on the circumstances. Cook's notes indicate that he may have considered it a panacea of sorts, triggering a bunch of different stuff that helped overall health, but keep in mind this was something to tune of 150 years ago, so the information he was working with may have limited the scope of his understanding. For all his otherwise infamous reputation, his work aboard the Belgica was nothing short of pioneering for the time. His life after that expedition over-shadows any positive contributions to science he made, unfortunately.
Vitamin D is not an outcome of standing by fire. It is from UV spectrum which is entirely absent from fires. It needs high temperature fire like fusion to be emitted. Totally doable by sun but not by your campfire.