I've had one for 3 years now, last year they upgraded me to the platinum card, guess I was profitable enough.
Originally I applied for Cathay's Sogo mall card and was turned down like you said, a foreigner with no guarantor. I leaned on Sogo mall for help to no avail. Applied for the new Costco card when it came out and was rejected again but the saleslady at the branch called and gave them what for and it was approved.
From the stories I read, a lot of people that were rejected complained to Costco and the rule was changed. And to be honest, from a risk prospective, I would think Costco members would be a good risk, these are people willing to pay money to shop at a store that really isn't that cheap.