Also, there's the idea that it's the responsibility of states and navies to provide security. I would think it's a step backward if we start privatizing security of the shipping trade.
That's my take on the situation as well. Note, that's nothing against the crew or owners of the Alabama, but that's me as a former Navy sailor feeling disgusted by the prospect of the Navy not doing its primary function. Protecting shipping is the reason the Navy exists and right now, it isn't doing that. Whatever disease modern society has (probably simply a bad case of PC) that has softened it to the point of impotence, there is a reality here that won't go away by trying to treat it differently:
*someone* has to shoot pirates and sink pirate ships. Since the Navy isn't doing it, private shipping companies are now doing it. In other words, by shirking their responsibility to be navies, the navies of the world are forcing private shipping companies to become navies.
Even the handful of times pirates have accidentally attacked Navy (not just US Navy - they seem to have a thing for the French), they've been warned off or arrested. That's just not the proper way to handle the situation.
See the currently active thread in the politics forum on the prospects of arresting Bin Laden for a similar complaint from me about using the Army as police instead of as an army.
[edit] The article says the Alabama is being "monitored" by a P-3 Orion. The Orion is capable of carrying torpedoes, long range air to surface missiles and short range Zuni rockets. I see a straightforward problem and several potential solutions...
And as a more complete solution, the coastline including the gulf of Aden runs about 1500 miles. You could cover the entire area with 3 patrol planes, requiring no more than an hour to intercept a ship under attack off Somalia.