Since the Fed is the provider of the liquidity and also sets the rules on what is a collateral and what is not, I say yes, the bank must loan you the money as long as you satisfy the conditions of the loan.
The bank is roughly a re-seller of the Fed liquidity. They shouldn't be an arbiter of who gets to access that liquidity but rather an administrative entity that follows the rules.
That doesn't make sense. When your business account stiffs a bunch of customers who get their ACH transactions reversed, and you're insolvent, your bank has to pay off those transactions. It can't just go to the Fed and say "give me money to cover for this insolvent business".
Your bank is not in fact literally just a front end for the Fed.
The bank is roughly a re-seller of the Fed liquidity. They shouldn't be an arbiter of who gets to access that liquidity but rather an administrative entity that follows the rules.