Anon--I wish this were a question of technology. In many cases with the larger banks, especially, it is next to impossible to get in touch with someone who will verify that the check was issued by their institution. Most smaller banks still do this, but an increasing number of larger banks have discontinued this practice. In a normal situation, I would contact the issuing bank with a check number, payee, and amount to verify not only that the check was issued but that the check has not been altered. This is a common practice in the industry, but as I stated, it is not always practical or even possible.
Regarding the suing of your bank: Feel free. There is nothing to stop you from initiating such a lawsuit. However, you will still be held liable for the money because you initially received benefit from the check and there is no requirement for your bank to guarantee the funds on this check.
What is stopping them from investigating you for the possible knowledge that this checks was counterfeit? It sounds ridiculous from your standpoint, I know, but not from your bank's, especially with your refusal to accept the loss.
Regarding the public knowledge of counterfeit checks: How is is that far-fetched to expect a reasonable person to believe that a piece of paper can be printed in such a way as to resemble a cashier's check? How long has currency been counterfeited? Would it not be more difficult to copy the intricate patterns and colors found in money than to copy a check?
You're going to do what you decide is the right thing to do. I can't change that. If your bank acted wrongly, I hope a remedy is found. But again, please take this as your education about this topic and don't be shy about sharing your experience. That is the only way that your friends and family will know how to handle a similar situation if and when it happens to them. I'd educate everyone on the planet if it were fesible, but it's just not.
(stepping off the soapbox)
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"Droplets of Yes and No in an ocean of Maybe."--Faith No More