So the Virginia teen, who has battled Ehlers-Danlos syndrome (an inherited connective tissue disorder) since she was 15, began talking with the Tim Tebow Foundation, hoping to get some face time with the former NFL quarterback.
She got way more than she bargained for.
Before she knew it, Burke and her family were flown to Scottsdale, Arizona. For four days and three nights, they stayed in the presidential suite of the Fairmont Scottsdale Princess Resort. There was a day at the spa. There was an aerial tour of the Grand Canyon with Burke acting as co-pilot. She even threw out the first pitch at an Arizona Diamondbacks game.
And then, Burke got her simple wish, spending time with Tebow during one of his training sessions. At dinner that night, they were surprised by Tebow again, who shared a meal with the teen and her family.
"They're amazing," Tebow, 27, tells PEOPLE. "The entire time I was with them, I was so inspired by their strength and courage in facing every day and every struggle with a positive attitude." (For her part, Haley was delighted, and immediately changed all her social media profile pictures to a photo with Tebow.)
As it turns out, Burke was a recipient of the Tim Tebow Foundation W15H program. (It's pronounced "Wish," but the "15" in the middle is a nod to Tebow's jersey number.) The program provides once-in-a-lifetime experiences to children and teens facing life-threatening illnesses.
"The W15H program allows me to keep a great perspective on life," Tebow says. "I always begin the wish hoping to have a positive impact on these children, but every time, I'm the one who has been impacted the most."
In addition to the W15H program, the Tim Tebow Foundation has an adoption aid program, builds "Timmy's Playrooms" in children's hospitals around the world, and has built a five-story hospital in Davao City, Philippines.
"Other than my faith and family, my foundation is the most important thing in my life," says Tebow, a devout Christian. "It allows me to keep so many things in perspective, and it gives me the opportunity to bring people together to invest in the lives of children all around the world."
Tebow, who is single, currently works as a college football analyst. In March, he told PEOPLE that his celebrity status allows him to do more philanthropic work. "For me, life isn't about being recognized or having everyone know who I am," he said. "[Charity work] is much more important than being a celebrity."
And after granting Burke's wish, Tebow still feels the same way. "My goal has always been to bring faith, hope and love to those needing a brighter day in their darkest hour of need," he says. "I've been so blessed to have a platform where I can influence and, hopefully, impact these incredible children."