Your american friend is not the first I've heard of being detained for lack of poof of legal status. It is a common occurrence but since the squeaky wheel gets the grease, we are bombarded by whining accounts of unfair haitian detainment. Cry me a river!
It is recommended to carry proof of legal migratory status at all times. A copy will do most of the time but if the agent is not comfortable with you for any reason he might ask for the original. That is ok because since you are carrying a copy the agent will be more prone to help you produce the original.
A good trick is to email yourself a photo of your passport and entry stamp ASAP after you arrive. If you forget the copy, like in the case of your friend, you can access email from anywhere and retrieve it.