NEW YORK – Stephen Colbert’s “song of the summer” special was either a real-life corporate tiff over Daft Punk or the most elaborately planned – and funniest – corporate cross-promotion in memory.

On his Comedy Central show Tuesday, Colbert said he had Daft Punk booked to perform the hit “Get Lucky” that night. But he said that on the day before, fellow Viacom Inc., network MTV had pulled rank, claiming the French dance duo had agreed to perform at the Video Music Awards on Aug. 25 and make the show its exclusive U.S. TV appearance.

Colbert read a supposed email from MTV chief Van Toffler that said “my peeps” are “feeling funky on this one.”

“I don’t care what MTV allows,” Colbert said. “My audience gets the song of the summer if they want it and I don’t even need Daft Punk to choose my show over the VMAs to get it. This is Colbchella … and it is time to dance!”

At that, the song “Get Lucky” came over the loudspeakers and Colbert launched into what became an elaborate dance video that included Hugh Laurie, Jeff Bridges, Bryan Cranston, Henry Kissinger, Matt Damon and break-in appearances on “America’s Got Talent,” Jimmy Fallon’s “Late Night” and “The Charlie Rose Show.”

After a commercial break, Robin Thicke came down from the audience to perform his own summer hit, “Blurred Lines.”

Colbert had promoted the supposed Daft Punk appearance. The previous Friday, he had tweeted: “This Tuesday 8/6, don’t miss Stephen Colbchella ‘013: The Song of the Summer of the Century with special guest Daft Punk.” The music website Pitchfork said Friday that Colbert had told his studio audience July 25 about Daft Punk’s appearance. Pitchfork said it had confirmed the booking, although it didn’t cite a source.

But plainly, the “Get Lucky” video wasn’t something pulled together in a day to air instead of a Daft Punk performance. Fallon’s show had posted video of Colbert’s surprise entrance on the NBC show’s July 29 taping, where he briefly danced to “Get Lucky” and left the stage without saying why.

“I don’t know what just happened,” Fallon said. “Song of the summer, man.”

The “appearance” on “America’s Got Talent” was taped the previous Wednesday just before the show’s live airing from Radio City Music Hall.

Could “The Colbert Report” have planned to use the video in conjunction with a Daft Punk performance? Possibly, although Daft Punk would have had to agree to make one of its rare television appearances on a show where it was likely to be upstaged by a video to its own song.

Reached by phone this week, Daft Punk publicist Kathryn Frazier said she would call back. She did not immediately, and did not respond to an email or additional phone call.

Was there really an argument between the two networks?

Toffler’s representative, Kurt Patat, said MTV had no comment.

Comedy Central spokeswoman Renata Luczak would not comment and referred questions to Colbert’s publicist, Carrie Byalick, who did not immediately return a query.