Of course, this bank has been criticized for being somewhat lax on who they give accounts to, but the point still stands. I could have been anybody, and give any false address. *shrug*
Why should they give a damn who you are? IMO, it's none of their business. Hell, they're making $$$ on *your* deposits, it's time they stopped being such shits about it.
Mostly they are afraid that you will get checks under a fake name, and bounce a lot of them, which ends up costing them a lot of money, even though they don't pay off on them. (Most of the costs of any financial transaction system come from handling exceptions). They are also under obligation to provide accurate SSN or Business Tax-ID information to the government on any interest-bearing account, so that you are forced to declare it on your income taxes. Clearly there are other ways of preventing or insuring against the problems that arise from check fraud (such as not issuing checks), but the IRS requirements are out of the bank's hands.