Factual error: In the scene where the Navy Seals are riding in the cars, the VA state vehicle inspection can be read from behind. It read "6 13" for June 2013. This would have been correct for the period the film was made, but not for the time of the incident.
Factual error: When Phillips is aboard the lifeboat, Najee has a pistol pointed at him at one point. The pistol is a 1911, and the hammer is forward when pointed at his head. Najee then fires it, but the hammer was forward the entire time until he fires the pistol. The 1911 is a single action handgun, and will only fire when the hammer is back.
Answer: If they pay the pirates, it encourages more to try the same thing. Shooting them would discourage anyone else from attempting to use a hostage to extort money.