It's been almost 13 years since I worked at Bank of America, but as you know, it's a big place. There are many places this loan could have originated.
It could have originated in commercial lending, real estate lending, a banking center, the mortgage department, and so on.
Frankly, I am not sure any of that matters since I have never heard of Bank of America letting anyone "assume" a loan. (We're not talking about taking a loan subject-to, correct?)
If I recall correctly, there were FHA loans way back in the day that were assumable without any credit check or underwriting. At the time, finding these loans was real estate Nirvana. But those days are gone, I believe, not just via FHA but everywhere.
My take is that if BofA were going to let you assume the loan, they would do so only after conducting a full underwriting involving your personal financials. And if they are going to do all that, they would likely prefer to skip the documentation risk that exists with assumptions and just get all new paperwork, with you as the borrower.
Only if the existing loan had some juicy language in there that made it a winner for them to keep would I envision them letting you assume it, and why would you want that? Or if the rate were fixed and above-market, they might keep it in place. But again, why would do that?
So, the Reader's Digest version here, at least from my point of view, is that assumption of a loan -- especially in an institution that has a credit policy manual as big as an Oxford Dictionary -- is unlikely at best.
Please let us know if you discover otherwise. We're all here to learn.