The highest peak in Saudi Arabia is Jabal Ferwa at 9,856 feet above sea level. Add some padding for safe terrain clearance, instrument error and human error, and 15,000 feet looks like a reasonable transition altitude.
The highest peak in the contiguous United States is Mt. Whitney at 14,505 feet, so 18,000 feet for the transition altitude looks similarly reasonable. (Special rules apply in Alaska around Denali at 20,310 feet.)
In theory, the transition could be much lower for non-mountainous areas of both countries, but apparently their authorities believed that a uniform transition altitude was simpler and therefore less prone to errors.