For the W8BEN our understanding is that foreign customers do not have to provide us with a foreign TIN if they are from Australia, Bermuda, British Virgin Islands, or Cayman Islands, because those countries either don't issue foreign TIN's or because their country does not permit them to share their foreign TIN.
1. Are there other reason(s) that a foreign person would not provide a TIN? The W8 instructions seem to have an exception for customers that are not legally required to obtain a TIN in their jurisdiction of tax residence, but I'm not sure I'm reading that correctly?
2. If a foreign customer provides us an exception reason, can we rely on what they tell us or do we have a duty to do more research into the reason and make our own determination?

The closest guidance i can find is from the W8 instructions that say "If you are providing this form to document a financial
account described above but you do not enter a TIN on line 6, and you are not a resident of a U.S. possession, you must provide the withholding agent with an explanation for why you have not been issued a TIN. For this purpose, an explanation is a statement that you are not legally required to obtain a TIN in your jurisdiction of tax residence."

Completing the form correctly is the responsibility of the person signing the form under penalties of perjury,and not the bank, as long as it appears to be fully completed. There are no requirements that a payor validate the information provided. If you are uncomfortable with the completed W-8BEN, offer them a non-interest bearing account and your dilemma disappears. Unless you are in the business of providing interest bearing accounts to non-residents. many banks limit the account selection to non-interesting bearing accounts due to the IRS reporting requirements, back-up withholding requirements, tracking W-8BEN expirations, etc.