This site has some great information on Degus and insulin.
I'll post what it says, since it's short:
Degus can become diabetic very easily1, 36. You need to cut out all sugars from your degus diet. To find out more about diabetes, visit the ILLNESS section and the HEALTH FAQ.
Degus can develop islet amyloidosis1, 36. This means that the islets of Langerhans in the pancreas (the cells that produce the hormones insulin and glucagon which regulate blood sugar levels) can be prone to accumulate starch-like matter that reduces their productivity.
Degu insulin (the hormone that lowers blood sugar levels) and the C-terminal region of glucagon (the hormone that raises blood glucose levels) is very different from other, non-caviomorph mammals1, 122. This suggests there is/was some form of evolutionary pressure on blood glucose hormones in caviomorphs1. It has been shown that the Hystricognaths as an order have a highly divergent insulin structure24b (including a phenylalanine deletion at position B24 and insertion of two amino acids at the carboxy-terminal end of chain A122), and may not be able to store it in the usual way122. In fact, degu insulin is only 1-10% active in controlling blood sugar levels compared to other mammals24b. This suggests that degus are either unable to regulate their blood glucose levels, or have an alternative mechanism for doing so24b. This is entirely possible, as the glucagon molecule, which is absent in degus24b, has many amino acid substitutions that can affect physiology24b. Similarly, the degu insulin molecule also has amino acid substitutions122. Alternatively, it has been suggested degus compensate for the poor effect of insulin by increasing the concentration of insulin in the blood24b, or that degu insulin degrades more slowly (has a longer active period) than in other mammals24b, or that there are more and different insulin binding receptors24b. In effect, this means that degus CAN tolerate low levels of sugar but in a different way/at a different rate to other mammals. It is hypothesised that the diabetic predisposition of degus is a combination of genetic problems and an alternate regulation pathway. More information on the role of sugar in the degu can be found here.
This page has a little more info on Degu diets:
They also have some great info to help you visualize how Goos bodies deal with sugar in their diet. You can find the graphs here:
While they're not born diabetic, they are born prone to develop diabetes. Since they're small, it doesn't take much sugar to send them over the edge.
If you're going to give fruit, it's important to give their bodies plenty of time to metabolize it all back out, and for their insulin levels to return to normal, before giving them fruit again. If their insulin levels don't have time to return to normal, then it starts damaging tissue and organs.