Your reasoning makes sense. There's a fair amount of recent research (see "meditation" via Google Scholar) indicating that meditation does indeed reduce cortisol levels and hence that could be one pathway for its effects.

That said, mounting scientific evidence indicates that meditation also changes our brain structure in ways that have AFAIK not been observed with exercise.

For me my own experience would seem to confirm this. The benefits I observe from meditation are both qualitatively and quantitatively different from what I gain from exercise (both aerobic and heavy weights).