If you lose weight, and keep it off, and watch your diet and exercise properly, then you might be able to control your diabetes that way. However, make no mistake about it, YOU WILL STILL BE DIABETIC, you just won't have to take medicine. If you gain weight, or you don't exercise, or you eat too many carbs, then your blood sugar will rise again, because you will still be diabetic.
What your doctors mean is that if you control your diabetes, you won't get the blood sugar spikes. However, you will still be diabetic, you will just be managing it without medicine. Go ahead and ask them if this is so. And good luck with managing it.
If you don't manage it with diet and exercise, it can get worse. Even if you do manage it, you might need medicine when you get older. And you must, must, must watch your blood sugar, even when you feel fine, because your body might lose the ability to produce as much insulin as it used to, or you might not be watching your diet and exercise as well as you thought. You will need to check your blood sugar daily, or even more often if your doctor says to, until there is a good cure for diabetes.
There are oral medications that diabetics can take. However, insulin must be injected. If it's taken orally, the digestive juices will render it useless.
Incidentally, if you ever need an organ transplant, they can transplant the cells that produce insulin. This would be a cure for diabetes, but it generally causes more medical issues than it solves, so they don't do this unless the patient needs another transplant.