It's not really that complicated, but you can't just let "nature" take it's course -- there's no nature in your house. In nature your chinchilla wouldn't be chowing down on raisins, nuts, mineral and salt blocks.
Like people, animals will choose what tastes good over what's healthy. Virtually every species of animal alive can cause itself to have some sort of diet related health problems if fed whatever they want to eat.
We are as gods to the beasts of the fields. We order the time o' their birth and the time o' their death. Between times, we ha' a duty. - Terry Pratchett.
"Men have forgotten this truth", said the fox, "But you must not forget it. You become responsible, forever, for what you have tamed. - Antoine de Saint-Exupéry