But as the Americans slowly unravel the international network surrounding Osama bin Laden, the man they blame for the embassy bombings in Nairobi and Dar es Salaam, "blowback" is exactly what they are finding.
Last week, it was revealed that one of those under arrest is a former Egyptian soldier named Ali Mohamed, who is alleged to have provided training and assistance to Mr bin Laden's operatives. Yet Mr Mohamed, it is clear from his record, was working for the US government at the time he provided the training: he was a Green Beret, part of America's Special Forces.
Mr Mohamed's arrest seems to be part of a pattern, as the US slowly moves towards the realisation that many of those now arrayed against it with Mr bin Laden were once its allies in the war in Afghanistan. The two sides turned against each other as the war in Afghanistan unwound, and America, not Russia, came to be seen as the enemy.
The US poured cash into Afghanistan throughout the 1980s in an effort to defeat - or at least tie down - the Russians. Its principal ally was Gulbuddin Hekmatyar, a ferociously anti-communist and militant Islamist leader. The US and Saudi Arabia both sent about $500m (pounds 300m) annually between 1986 and 1989 to fund the mujahedin, and other rich individuals from the Gulf - including Mr bin Laden - spent an extra $20m every month. The US funded the construction of the camps at Khost which it attacked two months ago in response to the embassy bombs.
It had already been known that in those days, the US and Mr bin Laden were on the same side, but it now appears that America may actually have aided Mr bin Laden's organisation and even trained some of those who it now contends are "terrorists". Mr Ali may be the missing link.
It had already been known that in 1989, Mr Ali came to the New York area to train mujahedin on their way to Afghanistan. Those visits have put him in the spotlight once before: among those he trained was El Sayyid Nosair, who was jailed in 1995 for killing Rabbi Meir Kahane, leader of the Jewish Defence League, and, along with several others, with plotting to blow up several New York landmarks. At his trial, Mr Nosair claimed that the reason he had military manuals was that he was being trained by the US, not because he was intent on terrorism. It is uncertain whether Mr Mohamed came to New York on official business, but for some of the trips, he was a serving US Special Forces' sergeant.
Mr Mohamed met the men at the Al-Kifah Refugee Centre in Brooklyn's Atlantic Avenue, a place of pivotal importance to Operation Cyclone, the American effort to support the mujahedin. The Al-Kifah Centre and the associated Afghan Refugee Services Inc were raising funds and, crucially, providing recruits for the struggle, with active American assistance.
The other end of the pipeline was in Peshawar, where the Services Office co-ordinated the transit of people, equipment and cash to the mujahedin, and to Mr Hekmatyar in particular. The Services Office was run by Abdulla Azzam, a colleague of, and influence on, Osama bin Laden, and was part of Mr bin Laden's effort to back the mujahedin. Both the Services office and Al-Kifah were also linked to Sheikh Omar Abdel-Rahman, an Egyptian religious leader later jailed for the planned New York bombings.
The US took a benign view of this at the time. The operation was, after all, assisting in the fight against Communism. As Mr Mohamed's presence showed, those associated with the US military were providing assistance to Al-Kifah. The recruits received brief paramilitary training and weapons instruction in the New York area, according to evidence in earlier trials, before being sent to fight with Mr Hekmatyar. Even Sheikh Abdel-Rahman had, apparently, entered the US with the full knowledge of the CIA in 1990.
But by the mid-1990s, America's view of Al-Kifah had changed. It discovered that several of those charged with the World Trade Centre bombing and the New York landmarks bombings were former Afghan veterans, recruited through the Brooklyn-based organisation. Many of those the US had trained and recruited for a war were still fighting: but now it was against America. A confidential CIA internal survey concluded that it was "partly culpable" for the World Trade Centre bomb, according to reports at the time. There had been blowback.
How and why did the people behind Al-Kifah turn against America? The US cut off funding in 1991 to Mr Hekmatyar, both because the Russians had withdrawn from Afghanistan and because it had at last started to realise that backing Islamic fundamentalism was perhaps not the brightest idea the CIA had ever hatched. America had also gone to war against Iraq in 1991, and stationed troops in Saudi Arabia, outraging Mr bin Laden and other devout Muslims.
There also seems to have been a huge disagreement over Bosnia. In December 1992, a US army official met one of the Afghan veterans from Al-Kifah and offered help with a covert operation to support the Muslims in Bosnia, funded with Saudi money, according to one of those jailed for assisting with the New York bombings. But that effort quickly disintegrated, leaving a great deal of bad feeling.
There are probably only three people outside the US government who ever knew exactly what role the Al-Kifah refugee centre really played, and how far the US helped to build up Mr bin Laden's organisation. One was Mr Azzam, the charismatic Palestinian who ran the Peshawar operation. He was killed by a car bomb in 1989. The second was Mustafa Shalabi, who ran Al-Kifah. He was murdered in 1991. The third is Osama bin Laden, and he is not telling.
And the US government is certainly not about to explain whether it helped create what it now refers to as Public Enemy Number One.