No. (but ...)
The entry in the Actions in Combat table in the Rules Compendium really is confusing, since we find nothing in the grappling section that would indicate that it‘s possible to release a grappled opponent as a free action. So it is either a typo on page 8 or they forgot to add the appropriate rule on page 60.
As you already pointed out, once a grapple has been started, the only ways to cease from grappling are either to release a pinned opponent as a free action or to escape a grapple by winning a grapple (or escape artist) check. It doesn't matter who started the grapple.
You can escape a grapple by winning an opposed grapple check in place
of making an attack. You can make an Escape Artist check in place of
your grapple check if you so desire, but this requires a standard
action. If more than one opponent is grappling you, your grapple check
result has to beat all their individual check results to escape.
(Opponents don’t have to try to hold you if they don’t want to.) If
you escape, you finish the action by moving into any space adjacent to
Although the line Opponents don’t have to try to hold you if they don’t want to seems to refer only to a combat with multiple opponents, it should probably also be true, if there are only two of them. So it is possible to release an opponent (with no action at all needed), but only if that opponent is just trying to escape the grapple.
Also, you automatically "release" an opponent, if you are unable to maintain a grapple because you are unable to move into the target‘s space (starting a grapple, step 4). The rules don‘t say whether or not you must move if you are able. I think it‘s reasonable to assume that you are allowed not to move and consequently immediately let go of the target. Since moving in is a free action letting go should also be a free action. A creature with the Improved Grab special ability doesn‘t have this option, though.
When a creature gets a hold after an improved grab attack, it pulls
the opponent into its space.
In his Rules of the Game articles Skip Williams suggests an optional rule for releasing an opponent in situations when both (or all) involved in a grapple are willing to give up the fight.
Release Your Hold: Curiously, the Player's Handbook says nothing about
voluntarily relinquishing your hold on a foe, so here's a rule to
cover that. You can release your foe as a free action. You are still
considered to be grappling, however, unless your foe also decides to
release you at same time. If your foe does not want to release you,
you can escape by winning an opposed grapple check that you make
instead of a melee attack. (...)
This rule would also let you get rid of the unpleasant grappling condition immediately (on your turn) if your foe is unconscious, dead or otherwise unable to conduct a grapple.