There are absolutely some homeless people who choose to reject housing assistance and shelter programs. I know because I did some volunteering to help the homeless and met a handful of individuals that were happy to accept donations but refused to be committed to any program. They refused to have rules imposed on them by the shelters and preferred the freedom of doing as they please. One of these individuals has been homeless since the late 80's and seems quite content with his lifestyle. I'm not claiming this is typical, but there are certainly more people like him out there.