my brother is a diabetic

Is your brother monitoring his glucose levels at other times of the day, with his diet and being physically active?

The information I found says that:
- Exercising with blood glucose levels above 300 mg/dL is dangerous
- Exercising usually lowers blood glucose levels, but it can have the opposite effect and raise blood glucose levels.
- Did your brother check his blood glucose level a few hours after exercising? Walking a long distance may/may not have been a strenuous or intense workout for your brother, and blood glucose levels can drop a few hours after exercising. He can also check his levels every 30-minutes during exercising (if feasible).

Does his doctor know about his extremely high number? What was recommended?

Here is the detailed information I found from two credible sources:

How Exercise Affects Glucose Levels
"In most cases, exercise lowers blood glucose levels. As muscles do their work, they obtain energy from glucose stored in the muscle cells as glycogen. When these supplies of glycogen run low, glucose from the bloodstream is used as an energy source. After exercise, the body replaces the stores of glycogen in the muscle cells and liver, which lowers blood glucose levels even more. This drop can take place many hours after exercising."

"Exercise can also have the opposite effect and raise blood glucose. This usually occurs when blood glucose levels are too high (usually over 250 mg/dL) before exercising, which indicates that insulin activity is too low. In addition, very strenuous exercise can stimulate the liver to release extra glucose into the bloodstream, due to an increase in adrenaline."
[Source: Johns Hopkins]

Diabetes and Exercise
"-250 mg/dL or higher. This is a caution zone. To make sure it's safe to exercise, test your urine for ketones — substances made when your body breaks down fat for energy. Excess ketones indicate that your body doesn't have enough insulin to control your blood sugar. If you exercise when you have a high level of ketones, you risk ketoacidosis — a serious complication of diabetes that needs immediate treatment. Instead, wait to exercise until your urine ketones test kit indicates a low level of ketones in your urine."
"-300 mg/dL or higher. Your blood sugar may be too high to exercise safely, putting you at risk of ketoacidosis. Postpone your workout."
[Source: Mayo Clinic]

For more information:
American Diabetes Association

Does this help?