I did a Citi "Global" card application earlier this year - Citi Premier Miles cardholder in HK, with Citi Gold - approved instantly with a whopping USD2K credit limit (HK limit is USD43K....). Had to wait until 3 months after opening our bank accounts here. During the application process, in discussions with the credit check team, my banker had to repeat on multiple occasions that the application needed to be processed via the "global" process instead of the standard credit check.

Separately did an Amex Global transfer - cleared straight away for a USD10K limit.