“People actually think I’m racing to win,” he says. “I’m like, ‘Seriously?’ Forget it.” This talk of losing sounds foreign coming from his mouth. There’s a line in the Wilco song “War on War” that goes, “You have to learn how to lose/ You have to learn how to die/ If you wanna be alive.” Armstrong has survived cancer. He’s contemplated death, lost a testicle in the process. But losing? On that front, Lance Armstrong is still in training.

Sinatra and Dino? Totally gay.

Starsky and Hutch? Complete homos.

Butch Cassidy and the Sundance Kid? Without a doubt the original Brokeback Mountaineers.

At least, that is, in the eyes of a culture that mandates that men can’t be anything more than chummy. No hugging. No lingering ass-slaps. No men-only vision quests. And certainly no sincere declarations of brotherhood. That’s just gay. What some might call “bro-ing down” or “bonding,” the all-seeing, all-knowing powers-that-be call “latent homosexuality.”

So what to make of Lance Armstrong and Matthew McConaughey? “LiveStrong” and “J.K. Livin’.” They’ve known each other for eight years, but only recently have they been joined at the sweaty, spandexed hip: trolling Sky Bar with drinks in hand, strutting the red carpet in Hollywood, running along the pier in Miami Beach, pedaling shirtless down the Pacific Coast Highway. Each appearance was slobbered over and speculated on in lowest-common-denominator bulletins like People, Us Weekly, and In Touch. Once Jake Gyllenhaal made it a threesome, eyebrows were raised like flags on Memorial Day.

Are these guys gay?

“We tried it,” McConaughey says in a deadpan drawl. “Wasn’t for us.”

He’s calling from behind the wheel, creeping along Cesar Chavez Street on the way back to his trailer-park abode on the outskirts of Austin, Texas. He’s been dealing with the distorted reality of the spotlight for 13 years. But back in L.A., Armstrong—whose dominance of the Tour de France was so total that it sometimes seemed as if he were toying with the rest of the field—has trouble with a 24/7 paparazzi monitoring system that might potentially portray him as anything less than a 10-speed He-Man.

“Our friendship just kind of developed,” Armstrong explains, brow furrowed. “He got out of a relationship [with Penélope Cruz]; I’d just gotten out of a relationship. I think people see pictures and they think we’re these overgrown frat guys, but we all have those kinds of relationships—and relationship isn’t a bad word. I mean, we all have buds, we all take guy trips, but you take something very normal and you put it in a magazine, and people start talking. It’s like, either you sleep with anything that moves or you’re gay. They can’t figure it out.”

McConaughey says Armstrong’s first problem is that he lets it get to him. His second: “He goes online all the time. Checking out things. Looking up things. I kick back and let things happen—I choose to stay unplugged.”