Either way, Odom wasn't on hand when the national team pool assembled Thursday in Las Vegas with 15 remaining players vying for 12 spots on the Olympic roster. They will practice until Saturday, when the three cuts will be announced, and then have a short camp and exhibition tour together before leaving for England in two weeks.
Odom is hardly the only player who opted out of the honor this year, although he's one of the few who didn't claim an injury problem. Also missing, for various injury issues, are Dwyane Wade, Chris Bosh, Dwight Howard, and Derrick Rose.
The roster that remains - anchored by LeBron James, Kevin Durant, and Kobe Bryant - is still very good. Even the bubble players, including Andre Iguodala, who has become a defensive dirty-work specialist for the national team, is impressive.
But 20 years after the original Dream Team, when NBA stars first embraced the Olympic movement (as long as that didn't entail staying in the Olympic Village), the whole thing is starting to feel a little stale.
It's not that a gold medal is guaranteed. Other nations can jump up on a given day and give the United States a game. USA Basketball has learned how to put together a roster for the international game, however, mixing working-class heroes in with the all-stars.
That lesson was learned in 2004, when Larry Brown coached a team led by Allen Iverson and Stephon Marbury in Athens. The roster included a 19-year-old James, and veteran presence in the form of Tim Duncan, but the direction of the team was scattered, and the United States was 3-2 in group play before getting bounced in the semifinal round by Manu Ginobili and Argentina.
The United States shot just 38 percent in being eliminated for the first time since 1988 (pre-Dream Team), and you'll never guess who hoisted up the most shots and had the most misses. Well, maybe you would have guessed.
Since then, USA Basketball has made sure the national team doesn't rely on jump shots, or at least doesn't rely on jump shooters. The 2010 world championship team let Durant and Odom shoulder the load and was rewarded with the gold medal.
The formula is in place, and the current team will have the necessary pieces. It is accepted that Durant, James, Bryant, Kevin Love, Carmelo Anthony, Deron Williams, Tyson Chandler, Russell Westbrook, and Chris Paul are going to make the roster.
That leaves Iguodala, James Harden, Eric Gordon, Rudy Gay, Blake Griffin, and No. 1 draft pick Anthony Davis going for the last three spots. As usual, there is speculation that some of the selection decisions will have business overtones. Which players will attract more headlines and viewers? Which individual sponsorship deals might tip the balance? (The national team is outfitted and sponsored by Nike.)
On the face of it, adding Davis to the roster makes little sense, and not just because he suffered a sprained ankle at a Hornets workout this week. He wouldn't play much and brings zero international experience. But would people be more likely to tune into the games to see Davis in his first professional setting? Maybe so.
The business of winning Olympic gold is just that, after all, and Wade made a little stir earlier this year when he said the NBA players who take part should be better compensated. As it is, the Olympics are a paid vacation with some basketball thrown in, and the NBA stars have Olympic bonuses in their endorsement contracts that do give them salary bumps.
But if playing for one's country isn't thrill enough for multimillionaires without whining about it, maybe it's time to reexamine the idea of taking professionals to the games. It might be more interesting if FIBA, the international governing body for the sport, made the Olympic tournament an under-23 tournament. That's what soccer does, and nobody complains. It isn't an exact parallel, because soccer does it to protect the cash cow of the World Cup, but FIBA could lift the stature of its own world championships by adopting the same philosophy.
Regardless, it isn't easy for USA Basketball to keep alive the buzz that the Dream Team started in 1992. The training camp and exhibition sessions aren't that taxing - Welcome to Fabulous Las Vegas! - and then the tournament itself is an eight-game schedule during which you hope the players stay interested.
As for the folks back home, staying interested is a test, too. It wasn't that way 20 years ago, and maybe it is time to change something.
Contact columnist Bob Ford at firstname.lastname@example.org, or follow on Twitter @bobfordsports. Read his blog, "Post Patterns," at www.philly.com/postpatterns