Imagine that: The NYT runs a piece headlined: "U.S. Backs Free Elections, Only to See Allies Lose". It turns out, all over the Middle East (but especially in Lebanon) the public image of the US is so toxic, that even the hint that a candidate for election is "pro-American" can result in upset victories for the anti-American forces.
Simple democratic process: American blundering leads to popular ill will towards America. This leads to the electorate opposing pro-American candidates (or those perceived to be) and implicitly favouring anti-American candidates. Elections, therefore, lead to more anti-American governments, not fewer. The Bush Doctrine inverted: spreading democracy is harming America's foreign policy.
This is why I say the biggest failure in the post-9/11 world has been our inability to come to terms with political Islam. Of course we should have negotiated with Hamas when they won the elections in Palestine. The alternative isn't waiting for a more moderate faction to come to power -- the alternative is further radicalization, and convincing the Palestinians that we cannot be trusted in any case.
Two historical examples, which you can read however you like: In 1895, after their crushing victory over China, the Japanese were forced to give up their gains in Korea and Manchuria by European powers. No small amount of racism was at work here -- Germany, France, and Russia all refused to see Japan as an equal power with a claim to the spoils of a disintegrating China. European morality wasn't at work here* -- after forcing the Japanese out of Korea and Manchuria, the Russians went right in and gobbled up whatever they wanted. This was the first of many unequal slights the Japanese faced at the hands of the west -- including the obstinate refusal of the Europeans to agree to a racial equality clause in the Versailles Treaty after WWI. By the 1920s, the Japanese had been convinced that, no matter what Japan did, the Americans and Europeans would never allow Japan an equal position in the world unless the Japanese took it themselves by force. The Japanese feeling that the west simply couldn't be trusted led directly to the invasion of China, then later the broader Pacific War.
*Clearly, I don't want to seem like I think Japan had a right to conquer huge swaths of China. The point is that European racism and hypocrisy left a bad impression.
Example 2: After the French lost at Dien Bien Phu, Ho Chi Minh and the Viet Minh believed that they would soon be recognized as the legitimate post-colonial rulers of all of Vietnam. The west insisted, at Geneva, that Ho be legitimized by national elections in both the north and south of the country. The Viet Minh agreed, knowing that any elections would easily bring the Communists to power -- there was no national alternative to the Communists. But the South Vietnamese eventually refused to hold elections (at American urging) for exactly that reason. This duplicity left a lasting mark on the Communists, who would basically refuse to negotiate for anything less than total American withdrawal from Vietnam for the rest of the war -- a position to which the Americans were eventually forced to accede.
So yes, our actions actually matter. And our hypocrisy matters a great deal. The problem is, the western electorate (and in particular the US and Canada, I fear) have a deep and abiding amnesia about foreign policy. Worse still are the aspects of foreign policy that are conducted totally in secret. In the case of the Muslim world, our only real option -- if we're serious about democracy being a good thing -- is to negotiate with the elected governments of the Muslim world, including Hamas. Hell, forget democracy for a moment -- the Iranian government isn't wildly democratic, but it's the legitimate government of Iran, recognized as such by all sane countries.
In Palestine, we've instead gone through this bizarre Kabuki where we said the Palestinians had lived under Fatah corruption and autocracy for too long, so they had to hold an election. The election held, we declared that Hamas was illegitimate, and began working day and night to reinstitute... Fatah corruption and autocracy. Go us. Nobody seriously thinks this isn't going to bite us in the ass again, soon, right?