We show that the recent AMS-02 positron fraction measurement is consistent with a secondary origin for positrons and does not require additional primary sources such as pulsars or dark matter. The measured positron fraction at high energy saturates the previously predicted upper bound for secondary production, obtained by neglecting radiative losses. This coincidence, which will be further tested by upcoming AMS-02 data at higher energy, is a compelling indication for a secondary source. Within the secondary model, the AMS-02 data imply a cosmic ray propagation time in the Galaxy of <10(6) yr and an average traversed interstellar matter density of ~1 cm(-3), comparable to the density of the Milky Way gaseous disk, at a rigidity of 300 GV.