I have not misunderstood you. I get exactly what you are saying and my previous response is directly on point. What you are describing is a pleading requirement.

In the industrial strength version we had when I was first licensed, if the indictment alleged you stole a red car and the government proved you stole a blue car, you would walk because of a variance between the allegata and the probata. The variance, by itself, was deadly to the case.

Now, there has to be some showing of prejudice to the defense.

But what does this have to do with impeachment?

Nothing, of necessity, but I would argue that impeachment should follow minimal due process standards. Meaning that the articles should give fair notice of what CONDUCT will be proven (as distinguished from the meaning of that conduct). In the Trump impeachment, there was a general denial at the front end, but when the evidence was in there was no further effort to contest his conduct.

In a criminal case, it’s also fundamental that the pleading be specific enough that you could prevail in a double jeopardy plea if the government tried to come at you again. That’s not a realistic requirement in impeachment.

I would argue that the right against self-incrimination should apply in that the POTUS should not have to testify and if he does testify he can claim the Fifth to avoid some questions…but I would not take it where criminal law takes it and say that his silence cannot be used against him.

I would not apply the exclusionary rule in an impeachment because the policy positions that undergird the rule simply do not apply.

But all this is nothing but my raw opinion. It’s not at all clear how analogous an impeachment is to a criminal lawsuit. You are assuming they are identical.