Yeah, anything called "aspirin" is still going to be acetylsalicylic acid, and anything called "Al Quaeda" is still shooting at us and needs to be shot, but do these names really signal any deeper sort of affiliation anymore?
Why is it something that's so hard to believe? The precedent for a highly organized, inter-national underground group exists (Mafia, Triads, etc). The precedent for states funding such groups exists (just look at the U.S.'s history of funding militant political groups around the world!) What's so hard to believe about the combination of the two?
Maybe what makes it unbelievable is that the existence of Al Qaeda is incompatible with a particular world view, one that rejects the need for anti-terrorist military action and the international surveillance networks that support such action. It would sure be convenient if Al Qaeda were just a fiction.
My fear and suspicion however is that "Al Quaeda" has become a term that is applied whenever there are "people, who happen to be Muslim, who shoot at 'us'."
That may not seem like something that is worth worrying about, but I think it is. When we apply the term loosely like that we aren't just applying a term carelessly. When we do that, we are attributing all the past crimes that we associate with that name to the people that we are calling "Al Quaeda", whether they had any involvement in those past crimes or not. We are further creating a situation where "Al Quaeda" can appear from nothingness, with no connection to previous "Al Quaeda".
Hypothetical example of why I think this is dangerous: If we (for whatever reason) invade Malaysia, and Malaysian Muslims start shooting at us because we have invaded their country. The moment we apply the "Muslim who shoots at us? that is Al Quaeda" logic, those Malaysian Muslims then, in the eyes of the general public, inherit the crimes of Al Quaeda (say, 9/11). All of a sudden we aren't in Malaysia for "whatever reason", but because those darned Al Quaeda (you know, those "9/11 guys") are there, and they must pay for their crimes.
That's possibly true, but that isn't necessarily a problem.
I think an uncomfortable reality that westerners will have to eventually come to grips with is that militant Islam is a problem. Now, I don't believe it poses an existential threat to western liberal democracies, but it's an incredibly powerful unifying banner for culturally regressive movements all over the world. I do believe that these movements are a threat to progress in the countries in which they operate. If calling it all "Al Qaeda" gives us the wherewithal to combat it, that's not a bad thing, especially when those groups take up the banner.
As a university student in Bangladesh during the independence war in the 1970's, my dad had high hopes for the country. Over time, he has become bitterly disappointed by the country's cultural regression. Instead of seeing secular democracy flourish, as intended by the original constitution, the country is seeing Islamization. Women are putting on head scarves and extremist Wahhabi madrassas are sprouting up and terrorists are starting to operate: http://en.wikipedia.org/wiki/Jamaat-ul-Mujahideen_Bangladesh. When my family lived in Bangladesh in the late 1980's, it was poor and full of crime, but the most you worried about was violent protestors at labor strikes, not organized, armed terrorists.
There is something happening in the world and you can't wish it away.
But sometimes, it's not your responsibility to fix. I mean, at some point, you have to let the Bangladeshis fix Bangladesh, the Somalis fix Somalia, the Afghans fix Afghanistan and the Iraqis fix Iraq. I don't think it's up to America to go in and intervene where-ever we see Western values being violated. Not only do we not have the resources to do that, but, in many cases, we don't even have the moral authority to intervene. A lot of the time the reason the country is as screwed up as it is, is because we, the West, screwed it up. I mean, all these countries are the way they are because of Western interventions. It was the West that drew the borders of Pakistan and East Pakistan. It was the West that drew the borders of Afghanistan and tried to impose its vision of civilization on a locale that simply does not want such a thing. It was the West that drew the borders of Iraq, and it was the West who kept Saddam Hussein in power, as a balance against the revolutionaries in Iran (which itself was another creation of the West). And now you're saying that the West has an obligation to go in and fix these places? Please. The world would be grateful if Europe and America intervened less, not more.