A single rider will never ever be able to gain a minute on a hostile pack (the peloton) on a flat stage.
And just to make it clear why this is so: Drafting. A group can ride up to 20-25% faster than a single man alone because of drafting. Riders will take turns, doing really hard turns at the very front of the group, setting a really fast pace, then moving to the back behind other riders where you can draft and go at the same speed but with much less effort, letting you recover. The guy riding solo faces 100% wind resistance and can never recover.
It's why some riders will help other riders from other teams, for example - you never know when you may want other teams to either help reel in a breakaway group...or help keep a breakaway stay away (a team can sit at the front and control the tempo, keeping the pace 'just' fast enough to ensure that other teams can't attack while leaving the breakaway free). -- Straight Dope boards
Bingen & Nikane: Riders who don't follow the unwritten rules of the peloton end up being an outsider. And in the end riders gang up against them, unfortunately - the main reason that you just follow the rules. -- Daily Peloton
Cycling is a bit unusual in that there's an unwritten code of conduct that helps govern the group as a whole. They wait for one another, take pee breaks en masse, and lend each other food or water or even equipment or rides.
I can see how this evolved, with a small number of people always racing against each other. It's the same directors, same riders, same mechanics, same officials, all racing day in and day out against one another.
What you don't want to do is to get a bunch of riders mad at you. Like in any group of people you get some feuds. The Dutch teams notoriously feuded for a long time, with Jan Raas (director of Kwantum as well as other teams) fighting with Peter Post (of Panasonic). The feud got ridiculous, with each team riding so much against each other that they'd let a third party win major races.
Another feud occurred between a US team, Motorola, and a Dutch team, PDM (a separate Dutch team). PDM, after Motorola's actions upset them (Motorola signed Andy Bishop away from PDM), retaliated by working specifically against Motorola. Their then director even made references to these actions in the Tour du Pont coverage. He pulls up next to the Motorola director and point blank asks why Motorola is chasing a solo PDM rider. Motorola had no reason to chase - PDM's podium threat, Lemond's Z team, was leading the chase.
The Motorola director has no answer - he sounds like a kid caught with his hand in the cookie jar. The PDM director angrily replies.
"You remember what we did after Andy, eh?"
Then he floors it and pulls away, which, I have to admit, isn't very impressive when you're doing it in the anemic GMminivans lent to the teams for the race.
Of course, at that moment in the race, PDM was trying to break Z's legs, forcing the Z team to chase a PDM rider all over the countryside. Motorola stepped in, lent their tremendous power to the chase, and brought the PDM interloper back into the fold. Motorola didn't need to do that - the solo rider was well under control, and Z was plugging away steadily at the front, using up their guys, trying to time the catch so that there'd be little time for any counters.
Two different teams, one (Motorola) sticking their noses into a situation which didn't concern them (they just wanted the stage win, which they got), the other (PDM) doing their job. PDM had more significant aspirations - they wanted to break their GC rival's team, and they sacrificed a guy to do it.
It's all the unwritten rules of the sport. Motorola was breaking one; PDM was trying to enforce it. -- Sprinter della Casa