(CNN) Five days ago, President Donald Trump and a handful of congressional leaders got together to hash out the particulars of a bipartisan immigration deal. The meeting blew up. The deal was nixed. And Trump said something very, very intolerant/tough -- depending on who you believe -- about immigrants from African and Central American countries.

That much we know.

What remains up for debate is what, exactly, Trump said. While the specific word he chose is immaterial -- as I noted here -- the fact that the President of the United States as well as several US senators and a Cabinet secretary are offering up totally contradictory accounts of what exactly happened in that meeting is worth further examination.

That led to the a very strange and tense exchange when Democratic Sen. Dick Durbin cross-examined Homeland Security Secretary Kirstjen Nielsen during a hearing on Capitol Hill on Tuesday about what happened at the meeting they both attended last week.

Nielsen has said she didn't recall that word -- "shithole" -- being used by Trump, although there was "cussing" during the meeting by various members.

"I don't specifically remember a categorization of countries in Africa," she said, although she later added, "There was a lot of rough talk by a lot of people in the room."

Someone here is lying. Or, if not lying, then willfully misleading in their public statements to leave an impression that does not reflect reality. That's not an insignificant fact given that we are talking about the President and four sitting senators.

Let's go through the latest public statements about the meeting by the five major players.

* President Donald Trump

JUST WATCHED Trump: Democrats don't want DACA deal Replay More Videos ... MUST WATCH Trump: Democrats don't want DACA deal 02:01

Following the reporting that Trump had used the term "shithole countries," the Republican President sent this tweet Friday morning : "The language used by me at the DACA meeting was tough, but this was not the language used. What was really tough was the outlandish proposal made - a big setback for DACA!"

On Monday, Trump again seemed to suggest he didn't say "shithole." "Senator Dicky Durbin totally misrepresented what was said at the DACA meeting," Trump tweeted . "Deals can't get made when there is no trust! Durbin blew DACA and is hurting our Military."

Then, on Tuesday, White House press secretary Sarah Sanders seemed to cloud the White House stance on all of this, saying: "The President hasn't said he didn't use strong language, and this is an important issue, he's passionate about it, he's not going to apologize for trying to fix our immigration system." Double negative! (Related: I haven't not eaten an entire sleeve of Oreo cookies in one sitting.)

* Sen. Dick Durbin (D-Illinois)

JUST WATCHED Sen. Durbin: Trump said those hateful things Replay More Videos ... MUST WATCH Sen. Durbin: Trump said those hateful things 02:17

Durbin confirmed -- on the record -- that the reporting on "shithole" was accurate. "[Trump] said things which were hate-filled, vile and racist," Durbin told reporters last week in Chicago. "But I cannot believe that in the history of the White House, in that Oval Office, any president has ever spoken words that I personally heard our President speak yesterday." On Tuesday, Durbin reiterated that assertion. "I stand by every word I said about what was said and what happened."

* Sen. Lindsey Graham (R-South Carolina)

JUST WATCHED Graham: Trump discourse is 'embarrassing' Replay More Videos ... MUST WATCH Graham: Trump discourse is 'embarrassing' 00:46

The Republican senator said this on Friday: "Following comments by the President, I said my piece directly to him yesterday. The President and all those attending the meeting know what I said and how I feel." Then, in an interview with the Charleston Post-Courier on Monday , Graham added, "My memory hasn't evolved. I know what was said and I know what I said." That was a direct shot at ...

* Sens. Tom Cotton (R-Arkansas) and David Perdue (R-Georgia)

JUST WATCHED Senators' conflicting accounts of Trump remark Replay More Videos ... MUST WATCH Senators' conflicting accounts of Trump remark 01:24

First came this joint statement on Friday, denying that Trump said "shithole." "We do not recall the President saying these comments specifically, but what he did call out was the imbalance in our current immigration system, which does not protect American workers and our national interest."

Then, on the Sunday talk shows, both men went further. "I didn't hear it, and I was sitting no further away from Donald Trump than Dick Durbin was," Cotton said on CBS' "Face the Nation." On ABC's "This Week," Perdue added, "I'm saying that this is a gross misrepresentation, it's not the first time Sen. Durbin has done it, and it is not productive to solving the problem that we have at hand."

Add into that miasma this tweet Sunday from The Washington Post's Josh Dawsey , who initially broke the "shithole" story. "White House official told me tonight there is debate internally on whether Trump said 'shithole' or 'shithouse.' Perdue and Cotton seem to have heard latter, this person said, and are using to deny."

* Sen. Dick Durbin (D-Illinois) ... again

CNN's Jake Tapper asked Durbin on Tuesday about the Republicans challenging his account, and Durbin did not back down. He also argued it doesn't really matter if the President said "shithole" or "shithouse."

"Let me say they're wrong," Durbin told CNN's Jake Tapper on Tuesday in an interview, when asked about of Republicans who dispute his account. "I can tell you explicitly they are wrong. And let me also say, is that their defense, that S-House is acceptable, S-Hole he would never say? Come on. To think that the President of the United States would refer to any country on Earth as an S-House country, for goodness' sakes, what does that say?"

Those are the public statements from people in the room. Let me repeat: Someone here is lying. Or, if not lying, then willfully misleading in their public statements to leave an impression that does not reflect reality.

If Dawsey is right that the White House as well as Cotton and Perdue are hanging their denials of the "shithole" story on the fact that Trump said "shithouse countries" instead, well, that is the definition of a distinction without a difference. And it's not close to the "gross misrepresentation" that Perdue is trying to cast it as.

If Cotton, Perdue and Trump are right and Durbin and Graham are lying, then you need to ask yourself "Why?" Sure, Durbin can be explained away by the fact that he is the second-ranking Democrat in the Senate and is just hearing what he wants to hear to make Trump look bad and bolster his side's chances of winning back the congressional majority in November.

But, why would Graham lie? Why would he directly contradict both of his Republican colleagues as well as the sitting Republican President, whom he has grown increasingly close to in recent months?

And, if Graham and Durbin are the ones lying, why did Cotton and Perdue go from the equivocation of Friday's "can't recall" to Sunday's certainty that he didn't say it? What changed in their recollection?

One more piece of context: Cotton and Perdue are the co-sponsors of a more hard-line immigration bill they'd like the president to push if/when this bipartisan compromise deal collapses.

All of the arrows here seem to be pointing at the Cotton/Perdue duo. At a minimum, they should speak out and explain a) what changed between their statement Friday and their statements Sunday and b) why their story of what Trump said doesn't jibe with the version of events offered by Graham and Durbin.