The error is this logic is that it precludes the possibility that the Justice Department thinks (know for a fact even) that he is innocent but is pursuing the case anyway because political pressure from the President preferring him to be punished rather than admit a mistake.

Belief is not binary and can change with new evidence. You may believe it is likely someone is innocent, but should still witness all the evidence to update your beliefs. In the rare case that there is concrete and infallible evidence that the accused IS innocent, they are typically not prosecuted, or it wraps up very quickly.

This is the entire purpose of a jury trial. The intent is that the jury bears witness to all of the facts of the situation and listens to the prosecution's and defense's interpretation of those facts, and then decides whether the defendant committed any or all of the crimes they are accused of.

The potential source of error is the assumption that the president has the authority to stop a prosecution (short of the pardon power). I say "potential" because a "unitary executive" advocate would claim this is true, and it is becoming more true during the second Trump administration, although it was notably false during the first one. [In prior administrations, including Trump I and Obama, the DOJ appointed independent counsel precisely to prosecute cases the president would have disagreed with prosecuting.]