When Shoeless Joe Jackson was discarded by baseball, every hack in America knew the fix was in.

The facts said Jackson had not thrown the 1919 World Series, confessed before a grand jury, or been confronted on the street by a sobbing urchin demanding he "say it ain't so". But no-one cared.

The illiterate Chicago White Sox player, the best of his generation, was easy meat. His alleged betrayal made for a finer tale than a narrative involving chiselling nonentities, small-fry mobsters, nickel-and-dime owners, bought writers, or cheap bookies. Jackson was supposed to be better than all of those. For the tale to work, therefore, Jackson had to fall.

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I might be the last armchair cycling fan still to wonder about the quality of the charges levelled against Lance Armstrong. You can't argue with a man's confession. I don't argue, necessarily, with all the expert writers who told me, year upon year, that the doping had been witnessed too often, that the man was a bully, deeply cynical, and relentless in his conspiracies. It's just that I have old-fashioned ideas about rules of evidence.

There is still no positive test against Armstrong. That fact does not amount to exculpation, least of all when the fallen hero is on Oprah giving a half-story to keep the sponsors' lawyers at bay. He says now that he did all the things he always denied doing. He claims, in effect, that in order to win in his sport you pumped your tyres, supped your water and fixed your blood. Still: where are those test results?

Armstrong might have been a criminal genius. That's this year's story. It involves the belief that the International Cycling Union, those trusted with the Tour de France franchise, lots of coppers, every journalist, rider and fan, all the multinational sponsors, politicians from half a dozen countries and a raft of television networks, were intimidated – another word of the hour – by one big-mouthed Texan.

You are supposed to believe, first, that Armstrong brought money into his sport. That's then meant to explain why he got away with a massive criminal doping conspiracy and why, supposedly, no-one could bear to challenge the word of the lung-busting heroic cancer victim. Perhaps, instead, it better explains why the American was once useful to cycling, and then became one of those nasty accidents about to happen.

His story says something, I think, about heroes, and why heroes become necessary, or inconvenient. It has become hard to open a paper this week, for example, without encountering eloquent prose from someone who "always knew" about Armstrong. You'd think, on balance, they might have called the cops, especially in France, Italy or Spain, where doping carries criminal penalties. Perhaps those writers just forgot.

Most of those same poetic scribes were filing copy when Armstrong was racking up his seven Tour wins. Some of them – but let's spare blushes – were never done describing his cardio-vascular uniqueness, or how the man who beat cancer could always beat Col du Galibier, or how a clean rider would always conquer cheats. When a hero was required, Armstrong headed most lists. When sport demanded a villain, who better than a fallen "former hero"?

This week Travis Tygart, the prosecutor who has been making his name at Armstrong's expense on behalf of the United States Anti-Doping Agency (Usada), said of the bike rider: "If he's sincere in his desire to correct past mistakes, he will testify under oath about the full extent of his doping activities."

The point is fair enough. But you could as well ask Tygart why he didn't haul Armstrong into court, or why the federal authorities dropped their investigations when evidence, actual evidence, evidence you could place before a judge, was impossible to gather or state. You could then wonder about the place of public confessions in law, or in sport. Tygart has a dangerous affection for the idea of self-evident guilt.

Armstrong did it, though. He has settled that point, despite a couple of hesitations for the sake of Oprah's cameras, beyond doubt. Any man who calls an entire career "one big lie" has ceased to quibble. No doubt he took advice even on the use of the phrase. But still I wonder about innocence, guilt, proof, heroes and villains.

The entire global campaign against doping in sport has been built on science. We hear, time and again, that the crooks get more clever by the year. Never fear, they say – and said it again during London's Olympics – for truth will win in the end. Armstrong's confession therefore settles all arguments but one. Why is there no proof? Should you wish to expose a liar or destroy a hero, the detail matters.

All he did was ride a bike. All that Shoeless Joe ever did was bat pretty well. Should this matter to any child in need of a hero? Perhaps your infant should be told to stop making a fuss over overpaid footballers, or sponsored cyclists, or those who manage to hold up a tennis racquet. Perhaps these things have nothing to do with heroism.

Overlooked in the Armstrong affair is the meaning of deceit. In his tale, everyone cheated, but he won. Did that make him a worse cheat than the rest, or a bigger winner in a dirty game? Joe Jackson barely made a cent from cheating that mythical child out of his belief in heroes. But someone imposed a version of honour on Shoeless Joe.

I don't defend Armstrong. He doesn't need my help. In some versions of the tale, nevertheless, you might mistake his deceits for something important, or for a parable of morality in the real world. For that to be true, you would have to contend that sport really counts for something, that a bike rider caught doping is no different from a politician caught lying about a war. That would be foolish.

The heroes of sport matter precisely because they are not important. Their lies and cheating don't count. We call them inspirational because only children ought to be inspired. From my armchair, I watched Armstrong win each and every one of his Tours. Am I therefore betrayed because now he admits what ought to have been self-evident from the start? Which of us is stupid?

What counts is the meaning of deceit. Or rather, what counts are the things you can trust. It does not matter, even slightly, if Armstrong led some multinational interests astray. Telling children emerging from cancer that personal conduct matters, that adversity is an opponent to be overcome, that to live strong is to live well, is an issue of trust you can't talk away on Oprah. I think Armstrong knows it, too.

I got over heroes a while back. The idea is, in and of itself, foolish. Better to stick with proof, evidence, and what you can show to be true. It would have been nice to believe in Armstrong, once upon a time. But when you surrender to the fairy tale of giants, you declare yourself to be small.

Lance, it turns out, was just as human, just as weak, and just as frail as all the rest of us. No chemical will fix that problem.