Your doctor is correct to say that fructose is not an insulin secretagogue, ie eating it doesn't cause insulin to be released. But, it's not the full story. Glycolysis, the way Glucose is metabolised is different from Fructolysis, ie the way Fructose is metabolised. Glucose is metabolised widely in the body. Fructose is metabolised almost exclusively in the liver, to replenish liver glycogen and triglyceride synthesis.
This ultimately affects blood sugars though and refined fructose can lead to hypertriglyceridemia. Usually, as diabetics, we are trying to get liver triglycerides down and not wanting to elevate them. Refined fructose sources such as corn syrup should be avoided.
When it comes to the unrefined sources, ie fruits, as with starches, it depends on your own personal metabolism, the amount of damage you have as a diabetic, usually a big unknown, the amount of fruit that you eat and the type of fruit you eat. There are many studies on the effects on BG levels of different types of fruit. Tropical and sub tropical fruits tend to be not so good for diabetics.
Have a look at the table 3 in this paper,
A Study of Blood Glucose Response Following Temperate and Tropical Fruit Ingestion in Healthy Adults. You'll see that on a scale where glucose is 100, some fruits such as Green Pears are as low as 18 and bananas and grapes are in the 60s.
I stick to apples, pears, plums, cherries, berries and the occasional orange, which is the highest at 47. As always, quantity is a major factor.