The four were in Zintan so that Taylor could meet with her client, Saif al-Islam Qaddafi, to discuss his defense in the ICC case against him. The court issued an arrest warrant last June for Saif, as well as his father Muammar and former Libyan intelligence chief Abdullah al-Senussi, for crimes against humanity committed during the regime's brutal attacks on civilian demonstrators in early 2011. Now, the Libyan authorities claim that Taylor and Assaf exchanged documents with Saif, and had "recording equipment" with them during the interview. Neither activity would be unusual for an attorney-client meeting, but Taylor and her team are supposedly being investigated on charges of spying. Libyan authorities have said that they will be held for 45 days, and frequent references to "threats to national security" do not inspire confidence in their fate thereafter.
Libya is an important test for the International Criminal Court. It's a challenging case -- this is the first time the ICC has faced opposition to its jurisdiction from a national government that genuinely wants to try its accused war criminals domestically. But it's arguably exactly the sort of situation that the court was designed to resolve: a country with a recent history of violence and a national government interested in ensuring accountability. However, because Libya has only recently emerged from civil war, and the new administration has still not managed to disarm all the militias, the potential for violence to break out again is high.
The ICC staff members were arrested by a local Zintani militia beyond the control of Libya's new government, the National Transitional Council. The same militia has custody of Saif, and has been using him as a bargaining chip with the NTC, so the arrest of the ICC staff may simply be an attempt to secure more valuable hostages. This scenario is most likely to recur in other unsettled contexts such as Libya's, where the central state hasn't consolidated its monopoly on organized violence. Although more stable post-atrocity governments may be inveterate violators of the finer points of international law (not massacring ethnic minorities, for example), they are sufficiently interested in the good opinion of the international community to refrain from grabbing diplomatic staff and shaking them upside down to see if any toy surprises pop out.
The reason established governments wouldn't do anything like this is that Taylor and her colleagues were in Libya on official ICC business and are therefore entitled to diplomatic immunity. Regardless of what the Libyans claim the ICC staff members did -- and regardless even of whether they actually engaged in any wrongdoing -- they cannot be detained, investigated, charged, tried, or punished.
Diplomatic immunity may seem like a trivial matter compared to the weighty issues Libya has faced -- war and peace, dictatorship and democracy -- but, as the oldest and most inviolable principle in international law, how it's treated here will have ramifications far beyond Libya. At the height of the Cold War, the U.S. and the Soviet Union honored the immunity of each other's diplomats, even when those diplomats were suspected of being spies. The superpowers have been equally respectful of the immunities of less powerful states. In 2004, for instance, the U.S. State Department intervened in support of Robert Mugabe's immunity from suit during a visit to the United Nations, though Zimbabwe was under U.S. sanctions at the time. Even countries that are actively at war nearly always honor the immunity of each other's officials. Immunity is the sinew that binds together so much of international relations. Without it, diplomacy, treaty negotiations, and the very existence of international organizations would all collapse into impossibility. In short: it is a very big deal.