The English language is missing a word

This word would concisely and fully describe the relationship between two conclusions that are incompatible, one arrived at with evidence to support it, the other lacking this feature. It should also not be Latin. It shouldn't have elitist connotations. This word would replace 'disagree' in contexts like the following:

Report: EPA pollution plan won't cut it

The EPA's Office of the Inspector General said the rules should be written again after an "unbiased analysis" of how much mercury plants should be allowed to emit.
...
Agency spokeswoman Cynthia Bergman disputed the Inspector General's report, saying the inspector general simply "disagreed" with the EPA's approach. She said the agency would not redo the proposal and would make the rule final by mid-March.

Press Gaggle with Scott McClellan--Aboard Air Force One January 14, 2005

Q Does the President disagree with the report's conclusion that the war and the uncertainty on the ground has created a breeding ground for terrorism?

Press Gaggle with Scott McClellan--Aboard Air Force One November 20, 2004

MR. McCLELLAN: Well, we would strongly disagree with any characterization that suggested or implied that the way detainees are being treated at Guantanamo Bay are inconsistent with the policy that the President outlined. I'm not going to get into discussing specific reports by the International Committee for the Red Cross. These are confidential reports that are provided to the commanders on the ground -- and the incidents you're talking about, it would be to commanders in Guantanamo Bay. And we stay in close contact with the Department of Defense on these matters and issues that are raised, and to make sure that the Department of Defense is following up, or following through on those issues that are raised.

And finally, this longer bit shows why we need this word.

Press Gaggle with Scott McClellan--White House June 17, 2004

Q It is not consistent. They said this business on the nexus -- sinister nexus is not so.

MR. McCLELLAN: Where did they say that?

Q It's in the story.

MR. McCLELLAN: Okay.

Q No collaborative relationship.

MR. McCLELLAN: Go ahead, Terry.

Q Well, I'll pick up on that, if I may.

MR. McCLELLAN: Well -- and we never said that there was operational ties involved in attacks on the United States. Let's be very clear about that. The President talked about that just a short time ago.

Q What are people supposed to conclude, that they're having lunch with each other?

MR. McCLELLAN: A short time ago in his remarks.

Q You talk about deep, long-standing ties. What is that supposed to mean?

MR. McCLELLAN: Saddam Hussein supported and harbored terrorist groups --

Q Why don't you just say the commission is wrong?

MR. McCLELLAN: All right.

Q Well, because the terms that you did use, "deep, long-standing ties -- sinister nexus," and the President himself saying, "By removing Saddam Hussein we have removed an ally of al Qaeda," that means they are working together. Did Saddam Hussein and al Qaeda work together, where and when?

MR. McCLELLAN: I disagree with your characterization about --

Q Well, what does "ally" mean?

MR. McCLELLAN: But Saddam Hussein's regime and al Qaeda had a common enemy: It was the United States of America. And when you talk about a regime that has a history of supporting and harboring terrorists, and has a history of using weapons of mass destruction on its own people and on its neighbors, and then you look at the world through the lens of September 11th, the President made the absolute right decision to go in and remove that regime from power.

Q That's an argument. Those are not facts.

MR. McCLELLAN: One of the most dangerous --

Q That's just an argument. The facts as determined do not bear out that argument.

MR. McCLELLAN: One of the most dangerous threats we face in this day and age is the nexus between outlaw regimes with weapons of mass destruction and --

Q But you didn't find any.

MR. McCLELLAN: -- terrorist organizations. And the President acted, based on the information that we outlined, and that you can go back and look at. It's public information. Secretary Powell speaking before the United Nations --

Q Who has repudiated his own testimony.

MR. McCLELLAN: -- and Director Tenet testifying before Congress about these ties.

Q And just to button this down, the President stands by his statement that Saddam Hussein and al Qaeda were allies.

MR. McCLELLAN: Again, if you go back and look at the facts --

Q I'm asking what the President would say today.

MR. McCLELLAN: He stands by saying that Saddam Hussein's regime had ties to terrorism, including al Qaeda. And the basis of that is what I pointed out in Secretary Powell's remarks and Director Tenet's remarks. And that is consistent with what the September 11th Commission said. The relationship and contacts go back over the last decade.