The problem is that they (American military guys) might not see him as 'Royal' , but just as 'Hero Harry' who
fought was in Afghanistan so did his bit and is worthy of their respect. They won't know that he was protected by special forces and caused problems. Nor that much of his time in the military was spent travelling abroad for polo games and holibobbing in Vegas etc, or that his 'career' had been bought for him by daddy and granny because he was too thick to pass the entrance exams so they pulled strings.
WE see him as a Royal Prince (gone bad) but elsewhere they'll swallow the Hero Harry PR because they know no better and are having it shoved down their throats by none other than their presidents wife and she's a Doctor of summat or other. Allegedly.
Look at the image below. No6 with 'his boys'. Look at those guys, they are NOT squaddies,
those are seasoned hardened military guys given the job of babysitting the ginger baby. He looks like a lil kid among them. That's his military achievements, posing and Xboxing and being given leave for polo events and 3 weeks at Balmoral for Christmas with granny.
From a forces site.