Gizmag: "...starting from Kankakee, Illinois, and ending its trip in Rochester, Indiana."
In other words, left to right (->) in the map below. You can see that the altitude mentioned in the text box is 96,537 feet, or 18 miles. So at that point it is still attached to the balloon.
The paper airplane flight itself is just the right hand side curve, about 20 miles.
When I come to power, the headline writers will 'be the first against the wall.' LOL.