Indentity theft requires the con-man to as convincing a possible. So in the case of opening an account without your 3 months of bank statements, it is possible. The con just needs to be as convincing as possible and with some valid-looking documents it does help his cause.
Proving that you are who you say are is simply a bluffing game, a matter of belief.
Which brings me to another pet peeve relating to personal identity, that instituions have an infaliable belief in grainy fax sent documents - but a high resolution scanned PDF is somehow less legit?
Another interesting thought is that now there has been a surge of spoofing caller ids, see yesterdays news.
Having someone's contact detail and just a little bit of information about them, you could wreck a fair amount of havoc in their life.