This interesting, archived page https://www.webcitation.org/618QHms8h?url=http://www.fai.org/astronautics/100km.asp which I found in this answer to What would a "Kármán plane" look like, a bird, or a plane?, says:
In the early 1960´s, the U.S. X-15 Aircraft was flown up to 108 km. In that part of the flight it was really a free falling rocket, with no aerodynamic control possible. In fact, it was considered an astronautical flight, and the pilot got, as a consequence, his "astronautical wings", i.e. the recognition of being an astronaut.
A reading of this paragraph suggests that at or near this altitude, the X-15 had no attitude control available from aerodynamic surfaces nor propulsion (ergo the use of the expression "free-falling"). Was there in fact vector-able thrust available, or was it really just a hopefully-not-tumbling-very-much spacecraft near its periapsis? Or reaction wheels, or something else?