(CNN) -- Passenger David Martin knew the situation on Virgin America Flight 404 was unraveling Saturday when members of the flight crew began snapping at passengers.

One incident stands out for him from Saturday's flight, which spent more than four hours on the tarmac at New York's Stewart Airport after being diverted from New York's John F. Kennedy International Airport. Martin said he was rationing a limited number of cookies from first-class to mothers and children in coach when a passenger prone to outbursts asked him for a cookie. He was about to give her one when a flight attendant ordered her to sit down and told her she would not get a cookie.

"Everyone knew she was a very frantic woman, which is why no one said anything when she asked for the cookie. ... Everyone understood but the flight attendant," said Martin, CEO of the social networking site Kontain.com, who documented Saturday's travails using visual updates via the iPhone app to his Kontain account.

"I went to her and said, you need to understand that speaking to passengers like this is not going to do any good. You need to exercise leadership and responsibility."

Martin said the flight attendant dismissed his words, as did the pilot when he took his concerns to the cockpit.

See Martin's visual posts from flight on Kontain.com

Martin said the situation did not improve until the flight was finally canceled, 4½ hours after it parked at Stewart and nearly 12 hours after it took off from Los Angeles International, during which time passengers say they endured shortages of food and water, crying babies, panic attacks and rising tensions.

Severe storms and heavy winds paralyzed traffic entering and leaving JFK airport Saturday night, causing most flights to be diverted.

"Although we cannot control the weather or the circumstances, we agreed that we needed to have done a better job with making our guests more comfortable in a difficult situation," Virgin America spokeswoman Abby Lunardini said in an e-mail.

But if the delay had occurred a few weeks later, Virgin America might have faced more than $3 million in fines for staying on the tarmac for more than three hours.

Under the rule, which takes effect April 29, airlines could be fined up to $27,500 per passenger for tarmac delays lasting more than three hours.

Passengers were offered two opportunities to leave the plane after it parked on the tarmac at Stewart, and 20 of the 126 passengers chose to do so, Lunardini said. Internal policy dictates that Virgin America will never hold guests longer than three hours without the ability to leave the aircraft, she said.

"Although guests were able to leave the aircraft during Flight 404, if the ruling were in place we would have made the decision to cancel at the 2-hour mark instead of the 3- to 4-hour mark, which is our current practice," Lunardini said. "We are in full compliance with existing rules and are prepared to be in full compliance with the new ruling when it is issued."

The Department of Transportation is investigating the Virgin America incident, said spokesman Bill Mosley.

"The whole thrust behind the rule is to prevent passengers from being subject to that, to the delays in the aircraft," Mosley said.

American Airlines has joined JetBlue and Delta in requesting an exemption at JFK airport to the tarmac delay rule set, according to the Department of Transportation.

The closure of a major runway at JFK prompted the exemption requests, which would only apply to that airport for the duration of construction on the runway.

Even in situations when the flight cannot operate, the rule would ensure that passengers are allowed to get off the plane and return to the terminal, Mosley said.

American echoed the concerns of JetBlue and Delta in its JFK exemption request.

"Carriers, faced with increased operational difficulties as a result of constrained runway capacity just at the time the new tarmac delay rule goes into effect, and with the prospect of incurring $27,500 per passenger in fines, will inevitably cancel flights during challenging operational situations," the airline's DOT request said.

Martin said he supports the idea of fining airlines for delays as an incentive to ensure that other passengers don't have to endure the same experience.

"I would like on my left to be the CEO of Virgin America and on my right, the CEO of JetBlue to vouch with me for this bill," he said. "That's the kind of leadership that's required and demonstrates that these CEOs understand that passenger safety and customer service comes first."

Martin and his seatmate, "Dancing with the Stars" judge Carrie Ann Inaba, used Twitter and Kontain, respectively, to issue updates on their ordeal.

"Was stuck on a plane for five hours on a Tarmac. They ran out of food, a woman was escorted off by police and I'm grateful to new friends," Inaba tweeted at 11:14 p.m., after the flight was officially canceled and remaining passengers were led off the plane.

Read Inaba's Tweets

Martin posted intermittent updates to Kontain.com using his iPhone app while the flight was in progress.

"Tensions rising big time as we are grounded and passengers are trying to get off," he said in one post accompanied by a photo of passengers lining up in front of the cockpit to deplane.

"Virgin crew losing control of passengers. Police now onboard here," he said in a later post.

On Sunday night, Martin says he received a phone call from Virgin America CEO David Cush telling him that he'd seen his posts and expressing apologies.

Martin attributed his use of social media to convey the severity of the situation as a factor in Virgin America's decision to refund passengers the cost of the airfare plus a $100 credit.

"You can't just write in a complaint or call customer service anymore... social media, it's the only weapon," he said. "Airlines need to be more terrified of that than the actual bill, because they're going to have to compensate passengers anyway each time they get held up on the tarmac, but they're also going to lose passengers because their brand will be destroyed every time a passenger uses social media."