If I understand your question correctly, you are concerned about finding out what people are saying about you when they call a reference?
For most more established companies, a reference check does not include feedback. I am allowed to verify if someone worked for me, nothing more. This is a good thing for a bad employee, or someone who as you put it, left under bad political reasons, as there's nothing to be said about the issue.
Professional references are generally where the real info comes from. These are people you pick and even if you are asked for your last manager only, there's flexibility with the right approach (a former manager who can't speak isn't useful, one who left to some unknown isn't useful). If your professional reference is speaking poorly of you, there's a big problem in you and who you are picking. Generally this becomes obvious as the company hiring you is happy, gets to the reference check and says no thank you. They may not say why but it should be somewhat apparent.
Short of pushing for a reason you won't know for sure no matter what, you simply have to use your judgement, think about the context you left under, and pick your names properly (which is why the idea of references makes me laugh).