Isn't it more fraudulent to give the bank home-made documents than to give them nothing? At least when you give then nothing you're being honest about what you're giving them.
As for me, I continue to print out bank statements on university printers and have everyone from embassies to landlords accept them.
No one I've met believes that going to your bank's website and printing out the PDF they give you is fraudulent.
Turns out he had just gone through the whole debacle himself. He had to show a bank statement, but he only has an online account. Went to the bank to get a statement printed and stamped, and whoever he went to turn it in to still refused it because it hadn't been mailed.
Personally, I don't want to give the BA any easy reason to reject my visa applications, I get all the mailed proof of address I can.
The fact that they are so easily manipulated is the reason they are most often not accepted as proof of identification, regardless of criminal law. It could be totally legal and it would be in the best interests of banks/businesses to not accept them due to possible liabilities.
Also showing your current bank account statements will help.
But we'd rather refuse to open this simple checking account just because (...we're busy laundering money :-)...).
And no one gives you the exact goddamn reason or a simple solution.