If each charge is considered a different crime then double jeopardy wouldn't apply. Also, in the US at least, the justice system isn't about getting to the truth. It's about assigning blame for an act that is considered against the law. If you are charged with a crime then the prosecutor will prosecute you to the fullest extent of the law and do their best to win by getting a conviction. The prosecutor will not necessarily go out of their way to prove your innocence by attempting to get to the truth. Both sides present their case and the jury, or maybe the judge, make a decision based on what they've been presented, regardless of what the truth might be.