The reason why the label recommends an empty stomach is that it is important that the pill get a good dose of stomach acid to prevent it from releasing too soon. These forms of medicine that release and become active at various parts of the gut control the process chemically via pH. Some forms of budesonide are protected from releasing too soon by low (acidic) pH. If the pH is too high the medicine could release early and not be very effective.
Thus, the label is taking a conservative approach and maximizing the chances of proper release by keeping food, which could make the pH of the stomach less certain, out of the equation. Your doc apparently regards this as a minor concern. He may be right, but I always do everything I can to give my medicines the best chance possible to work.
When I took budesonide I took the pills immediately after getting up in the morning. This gave them about 30 minutes in the empty stomach while I showered and got dressed and went down to breakfast.