That's a valid point, but someone acting as a Federal prosecutor can only deal with legal bearing. Nobody on Mueller's team can publish a legal analysis based on "conduct and integrity."
When it comes to Congress, I am pretty sure Mueller nor his investgation team "publishes" any "legal analysis." Counsel simply turns over documentation to the House Judiciary Committee.
From that point, the committee reviews the material and determines if there is sufficient evidence to "impeach" the president. Conduct and integrity is determined along with any criminal act.
My point . . . Impeachment does not necessarily have to meet any judicial or criminal threshold or requirements.
Many say, and I wholly agree, the President has not committed any "criminal" act or as President, has the prerogative to execute in the manner he chooses.
I was old enough to follow the Nixon impeachment. Many, many people then as they do today with Trump, believed that President Nixon did not commit any act that would have been found criminally illegal. IT DID NOT MATTER. Same as today.
Charges against Nixon were 1. Obstruction of justice, 2. abuse of power and 3 contempt of congress. None of which Nixon would have been found guilty in a court of law.