There is no doubt that during the years in which Lance Armstrong was cheating (by "cheating," I mean breaking the rules against the use of certain substances or techniques), everyone else in the professional peloton was doing the same. Some got caught; some didn't. Of those who got caught, some (such as Jan Ullrich) got caught early; some (such as Armstrong) got caught late.
So everyone (for all intents and purposes) was breaking the rules. Suppose instead that everyone had been complying with the rules. Would the outcomes of the races (in particular, the Tour de France) have been the same? Arguably so. If everyone had the same drugs and devices, then everyone's performance ticked up at the same rate or to the same degree. Maybe this isn't technically true, but it's close enough for the sake of discussion and argument.
Of the two scenarios I mentioned (everybody cheating and nobody cheating), which would a cyclist prefer? Given the health risks of taking performance-enhancing substances, it's clear that a rational, self-interested person would prefer the scenario in which nobody is cheating. The problem is that nobody has any assurance that others will not cheat. If a particular cyclist suspects that others are cheating, he (or she, in the case of women's cycling) will be motivated to cheat, and the motive to cheat will result, in some cases, in cheating. I think this describes Tyler Hamilton. I don't think he wanted a competitive advantage on other riders. I think he wanted to be able to compete with the other riders on the same terms; but he knew that he couldn't do this without cheating. His cheating was reluctant and defensive rather than eager and offensive. It's possible that Armstrong falls into this category as well. He may have said to himself, "I know that Ullrich, Marco Pantani, Alexandre Vinokourov, and Ivan Basso are cheating, and I'll be damned if I race against them at a disadvantage." They, in turn, may have said the same about Armstrong.
In Hobbesian civil society, which emerges voluntarily from the state of nature (described by Hobbes as a "war of all against all"), assurance comes from the sovereign, who has absolute authority to punish violations of the law (which is promulgated and known to all). Cycling needed an authority with enough knowledge and power to punish transgressions of the rules—and to be seen to be doing so. This would have assured riders that they were not at a competitive disadvantage by riding clean. Some degree of self-policing would also have been helpful. If everyone had been vigilant about cheating and turned in those known (or suspected) to be cheating, the scandal might have been avoided.
Cycling will never be clean until it has a Hobbesian sovereign. Do you suppose Armstrong would be willing to play this role? He has the personality for it. He has the time and energy. He has a motive. It would give him purpose for the rest of his life and would go some way toward redeeming him in the eyes of those he betrayed. If not Armstrong, how about Eddy Merckx, Bernard Hinault, or Miguel Indurain? All three are towering figures in the sport (having won five Tours de France apiece), with impeccable personal and professional credentials. The problem is that they lack the personality for it (despite Merckx being nicknamed "The Cannibal" and Hinault "The Badger"), and Merckx himself may have used performance-enhancing substances.
