Look at the RESPA Reg X definition of "lender". Then look at 3500.21(b). If the broker is not closing in their name then the disclosure requirement for this disclosure does fall to the bank. But the timing requirement for disclosure is within 3 business days from the date your bank received the application, not at closing as your original post said was your practice. There are other disclosures that may be required at that point (within 3 business days) as well, such as the Good Faith Estimate, Settlement Costs booklet, early TIL, etc.
Jim Bedsole, CRCM, CBA, CFSA, CAFP
My posts - my opinions