It's perhaps even more instructive to look at the similar situation in the early '80s. The CIA was coming out with reports suggesting that the Soviet Union's military capabilities had been overestimated, and that the country was inevitably careening towards collapse. The then-emerging neo-conservative movement pounced on this analysis as weak on the USSR and coddling Communism and so forth, and persuaded Reagan to push defense spending into overdrive to counter the Soviet threat.
Ironically, both sides were, in a certain manner of speaking, correct. The CIA analysis was much closer to the truth, as it turned out. But it was America's defense buildup which pushed the USSR, desperate to keep up, over the edge into insolvency and collapse. The neocons had the right policy for the wrong (stated) reason. (Ok, it's impossible to dismiss a counterfactual--perhaps Reagan's defense spending wasn't really the best possible policy, or even the reason for the Soviet Union's collapse. We'll never know. But if you'd told the US in 1980 that the USSR and its satellite states would peacefully dissolve by the end of the decade in a wave of democratization, and all it would cost us was a couple hundred billion dollars extra every year, you better believe we would have leapt at the opportunity.)
I add "stated" because there are suggestions, in hindsight at least, that the neocons knew they were overestimating the Russian threat (or at least arguing that we should act as if the worst-case estimates were true), but did so to achieve a policy that was actually tailored just as well for the case where the USSR was going bankrupt, but that would not be sellable to the American people if they believed that.
I'm far too young to have a sense of whether this is at all accurate or just ex post facto covering up. I do see it as fairly clear that some of that consciously went on--among the neocon movement, which is mostly a bunch of intellectuals at think tanks and a couple magazine columnists, and which has no role in the upper ranks of the Bush government--in the lead up to this year's Iraq war. The real reason the neocons wanted to go into Iraq was to upset the political situation in the Middle East, to try to foster liberalism, democracy and economic growth throughout the region, to try to dislodge the Israeli-Palestinian conflict out of its rut and back towards a peace plan, to wean the US from its dependence on the terrorist-breeding fundamentalism exporting Saudis. To drain the Mideast swamp, and present its people with an alternative to terrorists and despots.
This isn't to say that Saddam, the degree to which he had WMD, and the degree to which he was allied with terrorist groups wasn't fundamental to the neocon argument. It was. But it was fundamental in the context of everything above.
As for how accurate that theory will prove, it is obviously way too early to tell. I do think the signs so far have been, on the whole, amazingly positive: the Iraqi people are happy to have had Saddam kicked out of power (although many are not too happy yet that it was the US that did it), and eager to establish a democratic government (although perhaps too eager, and pretty certainly without a good understanding of the rights, institutions, and checks and balances that are vital to stable democracy). There has been substantial progress on the Israeli-Palestinian front: while a real breakthrough is still very much in doubt, the peace process has been restarted, Arafat has lost much of his power and in particular his international legitimacy, reformists are gaining ground in the PA, the major terrorist groups have agreed to a cease-fire while Israel has begun a pullout from the Gaza Strip with discussions underway for a pullout from Bethlehem, Sharon has declared his desire to end the occupation (and indeed called it an occupation) and begun dismantling at least those settlements which are illegal, and the US, EU and Arab states are all generally on the same page (at least officially) and working towards the same short-term goals. Iran is undergoing its most intense pro-democracy protests since 1999, if not ever, and could be close to the brink of a democratic revolution. And governments from Syria to Saudi Arabia have made small but notable concessions toward democracy and human rights and against support for terrorism.
The much feared Arab "street" has not risen up in revolt against their leaders for playing along with the US' interests. Of course most Arabs do very much dislike US policy in the region and remain against the Iraq war. On the other hand, since the war there have been significant voices in Arab public opinion arguing that those among the Arab World who supported Saddam and/or Al Qaeda because they were opposed to the US have proven themselves both morally bankrupt and bad for Arab welfare. This is only the beginning of what the neocons argued we would see. But then, it is only the beginning; less than two months since Baghdad fell.
In other words, the neocon strategy certainly hasn't been proven right. But it has been proven plausible. We will probably find significant WMD activity in Iraq; we've already found proof that Iraq was in violation of UNSCR 1441. But it seems extremely doubtful that we will find existing WMD on the scale suggested by the Bush administration (as distinct from the neocons, many of whom didn't push this angle nearly so hard) before the war. Certainly we now have proof that the Bush administration either wasn't as sure about the quantities of existing WMD as it made itself out to be, or that their intelligence was wrong on these issues (or both).
Does that mean the policy was bad? No, not at all. Does it mean it was sold in an anti-democratic way? Possibly, yes. Of course almost every government policy is sold to the electorate, to some degree or another, by willful distortions. IMO at least some of the truth on this one was plain to see before the war, even (if not especially) by listening to the neocons who were pushing hardest for a war.
