Why did you leave your employment?

Consider this scenario:
You are being accused of been involved in alleged fraud (that truly never happened) because you acted ultravires (unknowingly because you have been doing it in the past without any body correcting you) with the utmost good faith. After a shoddy investigation, you were told to resign with immediate effect, which you did.
Another company has invited you for an interview and during the course of the interview you were asked: “why did you leave your last employment?” You answered: “I resigned”. You were further asked: “why did you resign?”
I your attempt to answer that, consider the following facts:
1. If you explain the true situation, there is the possibility that:
They might not believe your story thereby creating a doubt about your honesty
You might do the same thing (act beyond your powers) with them
2. If you economize the truth (i.e. tell a lie), what will happen if the prospecting company writes to your last employer to make inquiry about you and your last employer decides to spill everything out.
I urgently need an HR Pro or anybody to help me out.