The old 'rabbit starvation' is a myth that has been hanging around for a long time.
If rabbit were the only source of food in a person's diet they would, indeed, be malnourished. Same if beef were the only source of food, or beans, or only chicken and nothing else substantial. In hard times known to man throughout history, most recently being the great Depression (when many rural folks raised meat rabbits for the family), there were times when ALL there was to eat was rabbit - no bread, no veggies, no corn, no beans, nothing else. So these people did indeed starve. Hence the myth off rabbit starvation was sustained.
Just like the Atkins diet theory, a person who eats only meat will go into metabolic ketoacidosis and begin breaking down their own body mass to compensate for the lack of carbohydrates, fats, and fat-soluble vitamins in their diet.
In the time of the explorers, people were hungry as wolves when out in the wilderness and meals were infrequent. If you were a hungry pioneer and lucky enough to catch a large game animal such as a deer or beaver, there was fatty organ meat and fat-marbled red meat to be had. The cholesterol and saturated fat gave the hunter instant energy and the excess calories needed to recover from a period of hunger and exhaustion. Catching wild rabbits was not such a lucky deal, since they have so little fat the hunter would not have that extra boost of energy needed to recover from their hunger or to store as body fat for upcoming hard times.
In our modern world, we have fat calories available to us every time we blink an eye. We also have easy access to carbohydrates in many forms. Rabbit meat is an excellent solution to our modern diet dilemmas because it is so low in fat and high in protein.