There are mortgage brokers that will shop you a rate, or even comparison sites (eg LendingTree) and like insurance brokers, mort brokers will know what banks cater who which customers. Now, as before the crash, there will be different banks specializing in different products and if you include all of the information (which you ALWAYS should, nothing like getting a surprise 3 days before closing), then you will should not get crazy aggressive offers that you would not qualify for. The broker is typically paid by the lender and the broker is not interested in offering you products that you won't qualify for since it is a waste of time (they only get paid if you get a loan and you won't get a loan unless YOU think the terms are favorable to you).
After a few years, like 4 as the previous poster said (I have seen 2 years after a BK and FC) you can get a loan. I am not sure why your LO is saying it has to be off your report...you have to disclose it on the 1003 no matter what (there are 2 questions related to it, one is a 'in the last 7 years' question, the other is an 'have you ever' type question). In answering YES in the 1003 applications disclosures like I think it was VII B and VII E on the 1003, the LO is supposed to explain to the insurer why your new situation is different and why he/she thinks you will not default like you did last time. Maybe the LO doesn't want to do that or that bank has a policy not to bother explaining any yes answers.
You do not have to have every baddie off your report, just far in the review mirror and a more recent track record of fiscal awesomeness.
