Stan: we did that in Army Ranger School. I also did it in SF training. In RVN, we ate a lot of stuff. The Viets, didn't have much meat in their normal diet, so anything with meat was fair game and cooked in the field.
Back on point, one boils meat that is really tough to soften it up. The Viets did that with python for instance. Things like field rats were much like rabbit and cooked over a fire or in a makeshift oven created from hot rocks in the fire. I wouldn't boil rabbit. But has has been said, marinate could be helpful.
It's difficult to cook game over an open fire as the part closest get burned and the parts away don't cook well. One has to constantly turn or cover it. On one of my first SF field trips we killed chickens and cooked them. Just putting a stick in them and putting them over a fire didn't work well <g>. Also, we couldn't always have an open fire, it could be detected from too far away; so, a more controlled fire with a container over it to boil thing might be more a tactical issue.
Best,
Dave