As other mentioned, it all depends on the bank. My personal experience is with BCA, I just started a new job and they wanted me to open a BCA account, so went to the branch and during the process of opening the lady asked if my salary would be transferred to it, which I confirmed. She asked if I wanted a credit-card as well and made me sign on a blank application form. Didn't think much of it as I had tried previously to get a card (never with BCA though) but they always found an excuse not to give one to me as an expat, but this time a courier actually came to deliver the card to my office about 2 weeks later.
Like others I also get regular calls from other banks offering me their cards, I guess I'm on some kind of list since I already have one. I have actually tried to take them up on their offers a few times, but every time I said I would be sending my Passport/KITAS instead of KTP they said "ohhhhh sorry mister, this offer not valid for WNA" and they disappear.
Ahwell, just need the one anyway.