The short answer, from what I've seen, is the BI doesn't care who you put down as references. Common sense says you will only put those who will give you a favorable reference. The investigator will go to your old agency and ask for you personnel file, where all of you blemishes, screw ups, at-a-boys and performance ratings are displayed. Since you were fired you can bet there will be a detailed explanation in your file as to why you were told to leave. If the BI feels you are beyond redemption they will write it up that way.
We hired several people from a neighboring agency who were fired during FTO for officer safety issues. The issue was listening to the radio. The old agency used the radio almost exclusively, so there it was a big deal. Our agency used MDT or laptops and only used the radio for emergency or immediate need reasons, so people were less likely to tune it out. Most of the officers we hired after their termination were not bad officers, some were even good. Some even admitted to using the old agency to put them through the academy and doing what was necessary to get fired once they were in the FTO. The reputation of the agency was not a good one so it was not held against anybody for being fired from it.
But when a long train of abuses and usurpations, pursuing invariably the same object, evinces a design to reduce them under absolute Despotism, it is their right, it is their duty, to throw off such Government, and to provide new guards for their future security.
Translation for the intellectually challenged: If the government screws the people too much, it is the right and duty of the people to revolt and form a new government.