I personally encountered experience where no such option was provided. If you google around a bit, you might find I'm not the only one, and I kinda think that ain't a bug.
Also, the Facebook requiring me to send them copy of my ID might also not be accidental.
I used quite a time ago a secondary iTunes US account without credit card. And now at least in my (german) account I can also edit the payment option to "none". But perhaps this is a regional thing required by law or necessity here (very few people have credit cards because our banking system doesn't suck and money transfer is easy).
