Singapore

I got my H1 in Singapore several years ago. By that time I got my PR for about a year. My wife got her H4 at the same time. When I applied H1, I don't have any reference letters and my case got approved even without interview. I did have a HDB flat. But several of my friends without HDB flat got their visas too. I really don't know why you got rejected. This is the first time I heard a Singapore PR cannot get visa. Maybe F1 application is a different story.

Good Luck