Six weeks later, despite Hoffa and the Teamsters' dramatic exodus from the AFL-CIO convention in Chicago, the men were shaking hands on a deal to jointly represent thousands of customer-service agents at the then just-about-merged US Airways and America West airlines.
On Sept. 12, they agreed to take turns being president of the new group, the Airline Customer Service Employee Association-IBT/CWA. Cohen went first.
Why all the love? Call it a marriage of convenience. If the two unions hadn't devised a strategy, both stood good chances of being booted.
"We went over the math," Cohen said. "We said we should look at doing this together."
When the Phoenix-based America West Airline Holdings Corp. announced its acquisition of US Airways Group Inc. in May 2005, America West's management said its most difficult challenge would be integrating their two workforces - and two different unions - into one airline called US Airways.
But, because of the Teamsters/CWA alliance, integration has not been a problem for the customer-service workers, US Airways spokesman Philip Gee said.
"It is something unprecedented in the airline industry where two unions have joined together," he said. "In our case, they are the only of our labor groups that have reached a finalized agreement. No one else has done it."
The Railway Labor Act, which governs airline labor relations, says competing unions must come to some resolution or else petition the National Mediation Board for an election.
The election rules are complicated. A majority of the combined workforce, including furloughed workers, must participate, or the unions face decertification. With all the layoffs at US Airways, getting enough workers to vote would have been difficult, making the risk for decertification high.
This sort of situation can become a high-stakes battle even in the most straightforward situations.
"In a contest, you get a high likelihood of no representation, especially if the company works against you," Cohen said.
Besides, the situation with the CWA and the Teamsters was anything but straightforward.
In August 2004, the Teamsters won an election to represent customer-service agents at America West, but they then were unable to negotiate a contract. That left them vulnerable if their members became disheartened and declined to vote.
The CWA was not in a much better position at US Airways, although it at least had a contract.
But US Airways' workforce had endured one bankruptcy and was struggling through another, leaving its unions in the unpopular position of presiding over layoffs and drastic pay cuts.
"Faced with all that, it clearly made sense to work with the Teamsters," the CWA's Cohen said.
By joining forces, America West workers, who had no contract, were covered by the CWA contract and ended up with more money, the unions said.
"We made one organization," Cohen said. "We haven't had a problem since."
It hasn't been quite that simple for the other unions involved in the airline merger.
Andy Marshall, a top Teamsters official in Arizona who worked on the CWA agreement, said he appreciated the peace because, on another front, he's in an all-out war.
The Teamsters are battling with the International Association of Machinists and Aerospace Workers over which union will represent 6,850 mechanics and stock clerks.
Like the CWA, the machinists' union remained with the AFL-CIO.
And like Cohen and Hoffa, machinists' president R. Thomas Buffenbarger had a lot to say during the AFL-CIO split. He sharply criticized the leaders of the defecting unions, especially Hoffa's ally Andrew Stern, president of the Service Employees International Union and instigator of the split.
The finger-pointing and name-calling in Chicago didn't spread to Arizona, where Marshall says there is labor peace. He works well with leaders of the machinists' union in his state.
Elsewhere, "the Teamsters and IAM don't get along." But, he said, that's a product of a long history of turf battles, and not the result of the recent AFL-CIO split.
In fact, being on the same side of the AFL-CIO split is no guarantee of harmony, as was demonstrated in February when a melee broke out at the Philadelphia Airport Marriott hotel.
At issue? Which of two AFL-CIO affiliates would represent 8,000 current and furloughed baggage handlers at America West and US Airways.
In May, 22 members and officers of the machinists' union were arrested and accused of assaulting organizers from the Transport Workers Union. Affidavits described a brawl with broken glass and tossed furniture.
A preliminary hearing in the case is set for next Monday.
Despite the nastiness, the unions came to an agreement, again because they feared losing representation altogether.
The Transport Workers, which had represented America West baggage handlers, withdrew its request for an election, leaving the machinists' union at US Airways to represent the baggage handlers at both airlines.
Contact staff writer Jane M. Von Bergen at 215-854-2769 or firstname.lastname@example.org.