He told the aide to call back later: "I didn't want to crash and die in the bad weather."
Stone, 23, was understandably cautious, having come close to death twice in recent months.
His first brush with mortality - as one of those who subdued a gunman in August on a Paris-bound train in France - earned him an invitation to sit in the House gallery for Obama's nationally televised speech. The second near-death experience was in October, when he was stabbed repeatedly outside a Sacramento bar after intervening in a dispute between a man and a woman.
Still nursing wounds from both episodes, but back to work at Travis Air Force Base in California, Stone will fly to Washington as one of about two dozen people chosen to be Michelle Obama's guests because they personify - as the White House put it - "who we are as Americans: inclusive and compassionate, innovative and courageous."
This will be Stone's third trip to Washington since the train attack.
In September, he was honored at the White House and the Pentagon along with two friends - Alek Skarlatos, a specialist in the Oregon National Guard, and Anthony Sadler, a senior at California State University, Sacramento - who followed him down the train's aisle to tackle and disarm the attacker.
On a second trip, Stone participated in events at the Pentagon and the French Embassy, including a round-table discussion on the topic of homeland security.
"I should be dead twice now, so I just feel super relaxed," Stone said in an interview. "I have so many new friendships all over the country and all over the world."
Among the new friends is the French-American professor whose life Stone was credited with saving on the train, by using his skills as a medic to stop the bleeding from a gunshot wound to one of the man's arteries.
Stone did express one worry: that after two violent encounters in short order, he might be seen as a "brawler."
He said he could not discuss the Sacramento episode, in which a suspect had been arrested. "I'm a nice guy," the sergeant said. "I don't like to fight people."
After four years in the Air Force, Stone said, he plans to go to college, major in international relations and perhaps go into law enforcement, "maybe even politics down the line."