It sure seems like stealing. The cayman islands don't offer a tax haven for free. The corporation has to pay an annual license fee, based on the amount of capital. They also have to pay a bank or financial services company for various items. Many officers will visit the cayman islands partly for business, partly for pleasure.
All in all, financial services provide the bulk of the cayman islands economy. The primary reason corporations do business there is to avoid their tax where the money was earned or the corporation is truly based.
Since the governments where the corporation is earning money or based out of provide services such as roads, law enforcement, courts, etc. that make this income possible it is reasonable to assume that the regular tax is owed. The shell corporation is reducing or eliminating this tax, and a smaller amount is funneled to the cayman islands in the form of fees and so forth, much like a bribe to avoid paying tax.