Since gaining control of large swathes of Iraq and Syria, the Islamic State has stuck to a consistent pattern in dealing with hostages from the United States and the United Kingdom, two countries that adhere to a strict policy against paying ransoms. ISIS has produced and disseminated videos showing captives, including the American journalists James Foley and Steven Sotloff, executed under gruesome circumstances.

But the circumstances of the last remaining American hostage in ISIS captivity, a 26-year-old aid worker named Kayla Mueller, are different. On Friday, ISIS declared that Mueller, held captive since August 2013, had died after a Jordanian missile struck a weapons warehouse where she was being held. But the lack of physical evidence surrounding Mueller's alleged death has elicited deep skepticism from observers. Did Mueller die? And if not, why would ISIS say otherwise?

Here's what we know so far. In December 2012, Mueller, an experienced international-aid worker, moved to the Turkish/Syria border to work for the Danish Refugee Council and one other organization. In August 2013, she accompanied a Syrian man to Aleppo, Syria, where he was hired to repair a broken Internet connection at the Spanish chapter of Doctors Without Borders. The Syrian and Mueller, whose arrival in Aleppo was unannounced, stayed the night and planned to travel back to Turkey by bus the following day. They were intercepted en route.

Back in Prescott, Arizona, Mueller's parents received word that their daughter was alive. But the family asked the United States government not to undertake a risky rescue mission. Then, last July, ISIS demanded either a ransom of €5 million ($5.6 million) or the release of Aafia Siddiqui, a Pakistani imprisoned on terrorism charges in Texas, to free Mueller. The deadline arrived without either demand being met, and that was the last anyone heard about Mueller until Friday.

Skeptics, including the Jordanian government, claim the group's explanation for her death is unlikely. The photograph that ISIS published showed nothing but a flattened three-story building—there were no signs of smoke or of human casualties. ISIS claimed that none of its fighters perished in the attack, indicating that Mueller was by herself in the weapons warehouse.

However, witnesses have reported that Mueller lived in the same facility that housed the Islamic State's other 22 hostages. It meanwhile remains unclear why she would be placed in a warehouse without supervision.

The Jordanian government, among others, claims that these inconsistencies undermine the veracity of ISIS's claim. "ISIS is being illogical and they're lying," said Mohammad Al Moumani, a government spokesman.

Even then, this doesn't mean that Mueller is alive. Since ISIS first began executing hostages, the terror organization has not yet fabricated a murder. One possibility is that the group was unable to use Mueller's death for propaganda purposes, and instead is hoping to drive a wedge between Jordan and the United States. After ISIS published a video showing Muath al-Kaseasbeh, a Jordanian pilot captured in Syria last December, burned to death in a cage, the government of King Abdullah has launched a retaliatory bombing campaign against ISIS. But over the past two years, the Jordanian public has expressed unease with the king's war with ISIS, a fact that the terrorist group may wish to exploit.

Hussein Majali, Jordan's interior minister, said that this attempt would inevitably fail. "[ISIS] tried to cause problems internally in Jordan and haven't succeeded," he said.