Even with the newer glucometers which permit sample collecting on the arm, when checking for a blood glucose drop (hypoglycemia) one needs to test on the finger, because it is more vascular and the result will be more up-to-the-minute. The nurse who reported finding her sugar dangerously low after Michael's visit would certainly have stuck her finger.
Needle sticks on her arm could certainly have been caused by injecting her with insulin, which as mentioned by others, would leave no chemical trace in her blood. His trying to turn it around and blame her parents is typical of his whole approach, and a ridiculous attempt to cover his own guilt.