Does moving a grappled foe through someone's threatened area trigger an attack of opportunity?

Question

If one has grappled a foe, and then succeeds on a check to maintain it, one of the options is:

You can move both yourself and your target up to half your speed. At the end of your movement, you can place your target in any square adjacent to you. If you attempt to place your foe in a hazardous location, such as in a wall of fire or over a pit, the target receives a free attempt to break your grapple with a +4 bonus.

The attack of opportunity (AoO) rules state that:

Moving out of a threatened square usually provokes attacks of opportunity from threatening opponents. There are two common methods of avoiding such an attack—the 5-foot step and the withdraw action.

1. Does being moved out of a threatened square by someone else (in general, or while grappled) triggers an AoO?
2. If it does, would that trigger the "if you attempt to to place your foe in a hazardous location" clause?

Answer 1

Unclear.

There is no general rule concerning involuntary movement and whether it provokes AoO's, so let's look at some exceptions that might prove one.

Pull is an ability that involuntarily moves an opponent, and explicitly does not provoke:

Pull (Ex): A creature with this ability can choose to make a free combat maneuver check with a successful attack. If successful, this check pulls an opponent closer... Creatures pulled in this way do not provoke attacks of opportunity and stop if the pull would move them into a solid object or creature.

Roll With It is a goblin feat that creates involuntary movement, and explicitly does provoke:

Benefit: If you are struck by a melee weapon you can try to convert some or all of that damage into movement that sends you off in an uncontrolled bouncing roll... This involuntary movement provokes attacks of opportunity normally if you move through threatened squares, but does not provoke an attack of opportunity from the creature that struck you in the first place.

I'd be inclined to say that the "Move" grappling option does not provoke, because there are several other combat maneuver checks that cause involuntary movement which does not provoke (Reposition and Drag), unless you possess feats that do cause that movement to provoke (Greater Reposition and Greater Drag, respectively). Unfortunately, the Greater Grapple feat is unrelated and doesn't help here.

Expect table variation.