Chinchillas have very sensitive digestive systems designed to process very dry ingredients. They come from a desert environment where they subsist on dry grasses. If the moisture content in their food gets too high it gives them diarrhea. This can cause a cascade effect of digestive complications that can be difficult to manage and in some cases can be fatal.
The stomach and intestines must maintain a biome of organisms that exist at an optimum level for each stage of digestion along the bowels. If the bowel transit times are increased because of irritation or an improper mixture of fiber and water, that biome becomes disrupted. This can result in irritation of the lining of the bowels causing diarrhea and flushing the contents outward. This decreases the nutrients to the normal ratio of bacteria in the gut and new bacteria that are not necessarily the right kind will out-compete for the proper bacteria. This can cause a chain reaction that results in failure to digest food, more irritation to the bowels, and more diarrhea leading to dehydration, malnutrition, and death if it is not managed.
In some cases it can slow the bowels, resulting in a buildup of gas (bloat) which can obstruct the bowels. An obstruction effectively pinches off the intestine which causes disruption to blood flow, which causes the tissue to die off, and this can lead to perforation of the intestine and leakage into the abdomen, acute peritonitis, and even hemorrhage, all of which are fatal. And that is if your pet doesn't starve to death first because its system cannot process nutrients.
I'm not saying it will always happen this way but it's not worth the risk. Chinchillas should be fed a dry diet. The only exception is syringe feeding a sick chinchilla a specifically formulated food/water slurry, something that you might have to have do if your pet does not get a proper diet.