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.]