Initially, the chat was fairly banal — thoughts on the Super Bowl, mostly — but then the talk became more substantive, with a question raised about the senator's prospects for Super Tuesday, according to multiple reporters present.
When Obama noticed that the red lights of the journalists' recorders were on, including Zeleny's, he said that the conversation was off the record.
But Zeleny told Obama that he couldn't take the conversation off the record, just as more reporters crept out into the aisle to find out what was being said. After answering just a few questions, Obama returned to the front of the plane.
"In my view, whenever he comes back on the plane to talk to reporters, he is on the record," Zeleny wrote in an e-mail to Politico.
"We're not on the plane, in my view, to have private talks with presidential candidates," Zeleny added. "We're here to report what they are saying and give our readers a better idea of their campaigns and their candidacies."
"There has never been a press corps in the history of our nation that got as many interviews as they wanted," Jen Psaki, the Obama campaign's traveling press secretary, responded in an e-mail.
Coincidentally, a similar discussion took place on New York Sen. Hillary Rodham Clinton's plane at roughly the same time.
Whereas a candidate like Sen. John McCain of Arizona relishes lengthy on-the-record bull sessions with the media, Obama generally does not. So it's no surprise that reporters will rush to get a quote when he does so.
Of course, journalists griping about not getting enough access is nothing new — but as Obama and Clinton fraternize a bit more with the traveling media, and the rules aren't clear, it presents a problem.
Clinton, too, has recently made trips to the back of the plane — at times saying a conversation is off the record, even when there's little news to be had.
Balz said that it's "impractical" to try to have off-the-record conversations on a crowded plane full of competitive reporters and that even with such ground rules, news may still filter out on the Internet.
"Part of this is that neither Clinton or Obama did much of this in 2007," Balz said. "They didn't spend a lot of time schmoozing the press."
Balz said that the Clinton press corps had been discussing this issue of late, and it now appears the Clinton campaign is setting ground rules that conversations in the back of the plane are on the record.
Jay Carson, the Clinton campaign's traveling secretary, did not respond to an e-mail seeking comment on the campaign's press strategy.
Psaki did not respond to a follow-up e-mail specifically requesting the rules when Obama is in the back of the plane.
The Obama campaign did provide access to reporters this past week, including a Friday news conference and a talk with the candidate on the plane three days earlier.
Newsweek's Richard Wolffe said the question is not about access in general, but the "intense, unresolved debate about on-the-record, off-the-record stuff."
And it hasn't been an issue long, mostly because — unlike the Clinton campaign — Obama has been flying on the same plane with the media only for just over a week, toward the end of the South Carolina primary. Yesterday was perhaps the third time Obama ventured back, according to Wolffe.
For his part, Wolffe said it's not just an issue of the campaign staff disagreeing with reporters, because even reporters from different news outlets are divided.
A television journalist riding on the Obama plane said that the views of Zeleny, and Nedra Pickler of the Associated ress, do not apply for the entire press corps.
"The print reporters seem evenly divided, too," the television journalist said, specifically between those who insist that Obama always be on the record and those who think he should have the option of speaking without being quoted.
Not to mention, the journalistic caste system plays a part.
Print reporters ride in the front of the plane, followed by television media. So if Obama does talk for just a few minutes on the record, it might be within earshot only of the political reporters from, perhaps, The Times and Post.
Wolffe hopes that the discussion among the Obama press corps will lead to a negotiation with the campaign over ground rules.
The Clinton side now accepts, as of Saturday, that conversations between the candidate and reporters at the back of the plane will be on the record.
And on Sunday afternoon, it gave yet more ground to the press.
The Clinton team originally told reporters that only the first five minutes of the campaign-organized Super Bowl party, held at Dixie's Smokehouse in St. Paul, Minn., could be on the record.
But after reporters from The New York Times, The Los Angeles Times and The Chicago Tribune, among others, protested, the campaign changed course.
So if Clinton cheers an Eli Manning touchdown pass, you can quote her on that.