That is its range, not the altitude it will reach. I was confused about that point, too. I researched MANPADs for a book I am working on.
A Stinger might theoretically reach 13,700 ft, but probably not.
The book is a thriller. I wanted the bad guy to bring down a plane with a Stinger, but the plane would most likely be flying at 30,000 ft at that location. Even though the point from which the Stinger was launched is 4,000 ft, I decided to give the pilot a good reason to be flying low in order to be credible.
OK. At the time I remember someone talking about a two stage missile with an increased range.