From TFA: "Thirty seconds after leaping, he’ll exceed the speed of sound in the thin upper atmosphere by traveling almost 700 miles per hour."
The speed of of sound in the upper atmosphere is _not_ 700 miles per hour. That figure relates to the speed of sound at one atmosphere and normal temperatures and also has to consider partial pressures including water vapor. In the upper atmosphere, the speed of sound is much less.
Claims similar to this over the years that the space shuttle is traveling at Mach 25 are just as ill-informed, since the "mach" number is supposed to be based on local conditions, not at some hypothetical place on a beach (one atmosphere, nice temperatures). It is wrong to simply divide some velocity by the speed of sound at sea level and then apply it to conditions present at the object's location.