I wasn't thinking straight. I should've said that adding water would cause osmosis to occur and this to happen....
(The one on the right)
...because water would enter the cells - not just the blood cells, but surrounding cells. The problem with diabetes is that insulin is not produced and thus does not get target cells to release the glucose. Without treatment, there is a higher concentration of glucose inside than outside the cell. Insulin is a hormone which allows glucose to exit the cell.
If you treat the patient with water rather than insulin, the molecules that are small enough to diffuse through the membrane will end up leaving the cell, because of lowered extracellular concentrations, which is the problem arising from the first point your professor made. Consequently, water will rush into the cell. Most glucose will not exit the membrane (without insulin).