... leave the grapple (IIRC the initiator of the grapple can leave it as a free action)
It's murky, and, actually, contradictory.
Once you are "grappling", regardless of who started it, leaving the grapple requires an "Escape the Grapple" check - either an OGC in place of an attack, or an Escape Artist check as a standard action. The opponent can elect not to resist, and let you go.
However, the sequence of initiating a grapple has four steps.
1. AoO is provoked.
2. Grab. (Melee touch attack)
3. Hold. (Opposed grapple check) - if this is successful, you and your opponent are now "grappling".
4. Maintain. This is where you have to move into the opponent's space. If you cannot move into their space, you must immediately let go of the target, and begin again at step 1.
Since you are "grappling" at step 3, achieving a non-grappling state
should require an Escape the Grapple check, if your opponent doesn't want to let you go.
It seems that they've placed their "you are now grappling" line at the wrong step - you've secured a hold at step 3, but you shouldn't actually be considered "grappling" until step 4 is successful.
-Hyp.