It has only been one week since Navy footage of two stranded sailors and their two life-vested dogs introduced Jennifer Appel and Tasha Fuiava to those on dry land. After months of floating adrift in Pacific waters, Appel could finally set her eyes on a rescue boat headed in her direction. Facing the motorboat’s camera, she waved her arms in the air and blew an emphatic kiss.

Since their rescue, Appel and Fuiava have recounted a dramatic tale: of surviving towering waves in a tropical storm, of fending off 20-foot sharks that attacked their sailboat for six hours straight, of being rescued on what might have otherwise been their last day alive.

And it is a retelling the sailors are staunchly defending, even as parts of their story have come under scrutiny in recent days.

To start, the women insisted they overcame a storm with near hurricane-force winds on their first night at sea, the AP reported.

Records kept by the National Weather Service show no signs of a storm around that time. Those findings were backed up by archived NASA satellite images.

“We got into a Force 11 storm, and it lasted for two nights and three days,” Appel told the AP.

Appel and Fuiava said they faced the storm off the coast of Hawaii. But the only tropical cyclone recorded on May 3 was near Fiji, thousands of miles away. The AP reported that while small, isolated squalls can pop up, a three-day storm would be detectable via satellite and prompt messages warning the public of severe weather in the area.

The sailors, along with their two dogs, had planned to sail from Hawaii to Tahiti at the beginning of May. Their boat’s engine died at the end of the month, leaving the two adrift at sea ever since. After being rescued last week, Appel said she “did not believe we would survive another 24 hours in the current situation.”

But for all the story’s drama, the sailors have had to answer for seeming holes in their account.

On Monday, a spokesman from the Coast Guard told the AP there was an emergency beacon on board the sailboat that was never activated. Initially, the women said they were equipped with communications devices, including six different kinds that all died.

Phillip R. Johnson, a retired Coast Guard Officer who oversaw search and rescue operations, told the AP that he had “never heard of all that stuff going out at the same time.”

The women also did not mention having an Emergency Position Indicating Radio Beacon, which communicates with satellites and sends location information within minutes, even if dropped in the ocean.

But then in a briefing with the Coast Guard, Appel said she did have the emergency beacon with her and that it was properly registered.

“We asked why during this course of time they did not activate the EPIRB,” a Coast Guard spokeswoman, Petty Officer 2nd Class Tara Molle, told the AP. “She had stated they never felt like they were truly in distress, like in a 24-hour period they were going to die.”

As of Monday, the AP reported that the Coast Guard’s review of the case was ongoing, but that no criminal investigation was underway.

The AP reported that on Tuesday, the women still maintained they did not use the beacon because they had yet to feel they were in imminent danger. They said so in spite of the fact that upon being rescued, the women said they were doubtful they could survive another day and that they endured a shark attack lasting six hours.

That shark attack — in which the women described 20-foot sharks ramming the boat in a coordinated attack — is also being questioned by scientists who study sharks and their behavior.

Kim Holland, a professor at the University of Hawaii and a shark researcher, told the AP that he has never heard of the kind of prolonged, coordinated attack described by the sailors. Sharks might home in on a single food source, but there would be nothing attracting them to a boat hull, Holland said.

The women have also said they had been trying to flag down vessels and send distress signals for at least 98 days. But the AP reported that they now claim to have reached someone at Wake Island.

The list goes on. Appel’s mother, Joyce, told the AP that she called the Coast Guard less than two weeks after her daughter left for Tahiti to report her missing.

But the Coast Guard denied getting such a call, saying it only received a call from a male “family friend” on May 19, several days before Appel and Fuiava were set to arrive in Tahiti.

The women told the AP that they had a float plan sharing their course and other details with friends and relatives. But in an interview with the Coast Guard, the women denied filing such a plan.

Furthermore, the women initially said the crew from a Taiwanese fishing vessel — from which they were eventually towed — was friendly. But they have since backtracked to say they were worried the crew was going to harm them. They also said the fishing boat caused major damage to their sailboat by backing into it.

“I also believe that they knew they were damaging the boat,” Appel told the AP. “And if we couldn’t get additional help, that boat would sink, and they would get … two girls to do whatever they wanted to.”

The AP reached the captain of the fishing vessel, who identified himself as Mr. Chen. He said his boat — the Fong Chun No. 66 — received a mayday radio call but didn’t understand it.

They then saw someone waving a white object from a boat about a nautical mile away, he told the AP. The women aboard asked to use the vessel’s satellite phone and for a tow to Midway Island.

Mr. Chen’s ship towed the sailboat overnight. But come morning, the women wanted to stop the towing and call in a naval vessel. Despite offering to bring them onto the fishing vessel and provide food or water, they women refused any extra help.

The fisherman left the area after the arrival of the USS Ashland, a warship operating out of Sasebo, Japan, that tracked the women down and dispatched a rescue boat.

As the motorboat approached, the dogs aboard the sailboat began to bark, footage shows.

“Hey how are you doing?” called out someone from behind the camera.

In between kisses, Appel replied, “Good, how are you!”

Eli Rosenberg and Avi Selk contributed reporting.

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