And over the past 24 hours, it has become clear that to even have made the comparison was not only wrong, but insulting.
Sunday morning, some 18 hours after Chamberlain had warned Rivera in full view of reporters and fans about "shushing him," it was Rivera, not Chamberlain, who offered an apology.
It was Rivera, not Chamberlain, who assumed the responsibility for defusing the incident.
It was Rivera, not Chamberlain, who expressed true regret that it ever took place.
And it was Rivera, once again, who demonstrated that there is no one quite like him in professional sports.
And it was Chamberlain who once again demonstrated that he is a lot like too many people that we encounter every day, in every walk of life: Rude. Defiant. Self-absorbed.
And pathetically self-unaware.
In an ugly and embarrassing dugout incident Saturday night, Chamberlain was making it difficult for Rivera to conduct an interview, so Rivera politely asked his teammate to lower his voice. Chamberlain responded by warning Rivera not once, but twice -- in tones that contained a hint of threat -- "Don't ever shush me again."
There was only one apology that I can assure was issued Sunday morning.
That one came from Mariano Rivera, who took it upon himself to apologize to the media and the fans, because "unfortunately it happened in front of you guys, and it shouldn't happen. We apologize and we move on."
Meanwhile, Joba was as sullen and defiant as a teenager caught cutting school, insisting that a 27-year-old middle reliever publicly warning a 43-year-old man, who also happens to be the best who has ever done what he does for a living, was "not a big deal," that two professional baseball players arguing in front of fans was "not an issue in the first place," and rebuking media members who had the nerve to be within earshot when he issued his warning, "This is not a story."
He said he saw no reason to apologize to Mo -- "For what?" -- and delivered what to the Yankees should be the most chilling line of all, and a fitting epitaph to his Yankees career: "I wouldn't change it. I wouldn't change anything I do in life."
You can write off the rest of it as youthful, if mindless, bravado, and even the public reprimand of Rivera as a clumsy form of dealing with the embarrassment of being made to look foolish in front of his friends and family.
But for Joba Chamberlain to say he not only would not change what he said Saturday night, but would neither change anything he has done in his life?
Well, that points to an athlete, and a person, who just does not get it, who takes no responsibility for any of his misdeeds, and has learned nothing from his mistakes.
That is not the kind of person who is fit to succeed Mariano in any way.
What Joba Chamberlain showed himself to be is just another of the louts we run into every day in the street, the ones who think their conversations are the only ones that matter, their business the only business that needs attending to, their lives the only lives of any importance.
I was not present at the dugout incident -- I was in the pressbox writing pregame notes -- but I was given a tape-recording of Rivera's interview session.
It was shocking to listen to, in several respects.
For one thing, the quietly emotional manner in which Mariano discussed his meeting earlier in the day with the family of a 10-year boy who was crushed to death by a falling airport sign was truly moving.
But the experience was tainted by straining to hear over the sound of Joba Chamberlain nearby, virtually screaming at the top of his lungs, to people in the stands about mundane matters like meeting at the hotel after the game.
Indeed, he was shouting so loudly it was difficult to hear Rivera on the tape, even though the reporter was holding it right under Rivera's mouth.
That is what prompted Rivera, after a couple of joking references -- "Is he always this loud?" -- to finally ask Joba, politely and, I'm told, with a palms-down hand gesture to tone it down just a bit.
"Suave," Rivera said, using the Spanish word for "soft," or "smooth."
Joba, of course, is neither. And of course, he took offense, because whatever he was saying and doing was far more important than what Rivera or anyone else was doing.
At least to him, at that moment.
It was all about Joba and what he wanted to do, and Mariano Rivera, or anyone else, be damned.
Afterward, Joba alternately tried to laugh his way out of it, to hide behind his defiance, and to use his young son, Karter, as a shield. ("My son wasn't here and I was a little bothered by that.")
They were all transparent attempts to blame his boorish behavior on something else. That is a direct reflection on his character.
Is that the kind of person the Yankees should want to trust important moments in important games to?
The truth is, after bursting on the scene with the brilliance of a meteor in 2007, Joba Chamberlain has steadily burned out since.
Among the things he would not change, apparently, were his DWI arrest in 2008, his disparaging remarks to the arresting officer about Yogi Berra, his ill-chosen remarks about the manners of New Yorkers, his decision to jump on a trampoline so intensely that he broke his ankle, and his public declaration this spring, in spite of knowing that the Yankees had determined he is a middle reliever, that he would like to be a starter once again.
His recovery and return from Tommy John surgery have been admirable, but his performances have been erratic, and there is little doubt that we have already seen the best of Joba Chamberlain on the pitcher's mound.
But on an almost daily basis, we see the worst of him in the Yankees clubhouse: loud, obnoxious, faintly threatening.
Or, pretty much the way he behaved to Mariano Rivera on Saturday night.
About a decade back, a marginal outfielder named Chad Curtis made the mistake of publicly criticizing Derek Jeter. He soon was an ex-Yankee.
After this season, Joba Chamberlain will be a free agent.
Knowing Mariano Rivera as I do, I can almost predict he will try to convince the Yankees that Joba is a soul worth saving and a talent worth keeping.
But by now, we all know better.
In the same ballpark where Mariano Rivera's Yankees career nearly ended a year ago on the warning track, Joba Chamberlain's Yankees tenure surely did in the dugout, his mouth writing what will soon be the epitaph to a career that turned out to be no more than a broken promise.