If you look at the basic biology of how a chinchilla digests it's food, it would only make sense to stay away from sugary treats like raisins and other fruits.
Chinchillas are hindgut fermenters meaning that they need bacteria in their cecum to assist in the digestion of their food. Without these bacteria, a chinchilla could not digest their food properly. Chins need these bacteria to process their food.
The bacteria in the gut that are responsible for fermentation are sensitive to diet changes. Under normal circumstances there's a balance of bacteria in their gut some of which digest sugars and others that digest the rest of the food. When you introduce sugar into this system, it causes the sugar and starch loving bacteria to grow rapidly and causes the normal gut bacteria to die off. Now you have a chin who's gut is way out of whack.
The beneficial bacteria that under normal circumstances digests their food has been replaced with sugar loving bacteria. So now your chin is going to have issues with digestion.
So, if you only give say, on raisin or half a raisin a week, at that time, the chin's gut is going to get out of whack from trying to digest all those sugars. Their body is just not meant to digest sugars, it's made to digest plant matter and fibrous material.
I wouldn't go so far as to say that constipation and digestive issues are caused by the lack of raisins. To me that goes opposite of how a chin's body actually works if you look at the science of it. Although our chins of today are obviously different than their wild friends, I think it's safe to say that the wild chins are not finding raisins and other sugary material to eat and they aren't dealing with huge outbreaks of constipation. And in all reality, I haven't heard of too many people having issues with constipation without some other issue leading into it.