Is it true that diabetes can be controlled strictly by diet and exercise?

For many people, yes.
With Type 2 diabetes (which affects about 90-95% of people with diabetes), the body loses it sensitivity to insulin. Many people with type 2 diabetes can control their diabetes by following a healthy meal plan and exercise program. For some people, when diet and exercise is not sufficient, oral antidiabetic mediations and/or insulin may be recommended. Diet and exercise play a large role in insulin sensitivity and blood sugar levels. Your doctor may recommend for you to attempt to control your diabetes with diet and exercise before considering diabetes medications.
Type 1 diabetes (which affects about 5% of people with diabetes) is an autoimmune disease that destroys insulin producing cells in the pancreas. People with type 1 diabetes require insulin to control their blood sugar levels.