Seems like that would solve the immunity problem.
It's not (necessarily) about the foreign cells, but the genetic autoimmune condition, triggered by something, that caused their Type 1 Diabetes in the first place.
From this CDC page on Type 1 Diabetes
Causes
Type 1 diabetes is thought to be caused by an autoimmune reaction (the body attacks itself by mistake). This reaction destroys the cells in the pancreas that make insulin, called beta cells. This process can go on for months or years before any symptoms appear.
Some people have certain genes (traits passed on from parent to child) that increase their chance of developing type 1 diabetes. However, many of them won't go on to have type 1 diabetes even if they have the genes. A trigger in the environment, such as a virus, may also play a part in developing type 1 diabetes. Diet and lifestyle habits don't cause type 1 diabetes.
Not a doctor, but I'm guessing it's like Psoriasis (which I have), which is an autoimmune issue enabled by a genetic defect; people can have the defect, but no symptoms until triggered by something, like an injury. This is why drugs and treatments that suppress the immune system work on psoriasis. The difference here is that the autoimmune reaction in T1 Diabetes continually destroys the pancreatic islet cells where the autoimmune reaction in Psoriasis causes too many skin cells to be produced and more quickly than normal. Psoriatic Arthritis (which I don't have, yet anyway) is thought to be also caused by a genetic autoimmune reaction similar to, but slightly different than, that of Psoriasis.