What Lunar writes seems logical, in my case I had opened my bank account with my passport and a precaria visa good for a few months with ICBC (but facilitated by my employer here). I was never asked for any evidence of my immigration status, and my account continued working as normal (i.e. badly) for about 3 years until I gave up on them because I wasn't able to associate my DNI with my account. YMMV of course.