Yes, But It Can Be Hard to Set Up
As the rule you cited points out, you do not provoke OAs when falling. The trick is making sure that you're actually falling when you cover those last couple squares, rather than descending in some other manner.
Case 1: Any Flight with Explicit Falling
Different methods of gaining flight act differently. Some powers that let you fly or items that give you a flight speed explicitly say that you fall at the end of the movement if you don't end on solid ground, so obviously you can fly to the point above where you want to be then end the movement, and you'll fall.
Example: Airstriders (level 25 foot item from Adventurer's Vault)
Property: You take no damage from a fall and always land on your feet. You have a fly speed equal to your speed +2, but you must end each turn on a solid surface or you fall.
On a side note, remember that when you fall you end up prone and take 1d10 damage per 10 feet you fell (minus any damage you avoid through a trained acrobatics check) unless you have a way of avoiding these penalties (such as the aforementioned Airstriders), which may not always be better than provoking an OA.
Verdict: Does not trigger OAs.
(Thanks wax eagle for pointing out you have to be trained in acrobatics!)
Case 2: Flight Speed with Deliberate Crashing
If you've gained an actual flight speed somehow (such as Zephyr Boots, from Adventurer's Vault 1) then you can move to a point above where you want to be then drop prone as a minor action, which will cause you to crash.
DMG pg47, on Flying:
Knocked Prone: A flying creature that is knocked prone crashes.
However...
DMG pg48, on Crashing:
Safe Distance: A flying creature that crashes immediately drops a distance equal to its fly speed. If it reaches the ground, it lands safely.
You only start actually falling after this safe descent phase, and since this safe descent appears to count as flight, it provokes OAs as normal. This means that you can use falling to avoid OAs, but the point you crash from must be at least your speed above the spot where you want to start avoiding OAs, which means you'll need at least 1 round to get into position.
Verdict: Does not trigger OAs if you start the crash from high enough up.
Case 3: "Powered" Flight with Safe Landing
The problem is that most powers that let you fly a short distance say that you descend safely if you end the flight not on a safe surface. As with the crashing rules, this safe descent is not falling, and doesn't appear to contain any exemption from OAs. Thus, while falling is in fact a valid way to avoid OAs, not all powers that grant flight will allow you to fall.
Example: Windwalker (Genasi Windsoul racial power)
Effect: Fly 8 squares. If you don't end your move on solid ground, you float to the ground without taking falling damage.
Verdict: Always triggers OAs.
Yes.
There are no limits* to how high a pixie may fly, provided that they end their turn only one square above the ground. However, if they do end their turn above their altitude limit they fall with the consequences laid out for falling (1d10 damage/10 foot of drop).
*The theoretical maximum height a pixie may reach on their turn (with no extra movement trickery) is 8*3 + 1 or 25 squares high (run 8, trade standard for another run 8, action point for another run 8, +1 for starting height), that's 125 ft at the end of which they would fall. Falling says to subtract the creature's fly speed so that leaves us at 95 feet of fall, meaning 9d10 falling damage.
Best Answer
Id love to go in to the physics reasoning as to why this may work, but unfortunately your character is in the DnD world and physics doesn't always apply. The short answer to your question is No (flying a grappled target harder into the ground would not do extra fall damage).
The reasoning is twofold - grappled targets and falling/falling damage.
First moving a grappled target (from PHB pg195):
So your speed is probably halved when you are flying with the target. This has nothing to do with difficult terrain.
But more importantly (and even if your speed wasn't halved), at 60ft per move (120ft double move/round, which is 6 sec), you are traveling at 20ft per sec or about 14 miles per hour. When you are falling, falls are instant or at terminal velocity (this is DMs call as we are in the DnD world not earth), but in a nut shell, you fall much faster than you can slam someone. Thus there is an argument for taking less fall damage by flying someone into the ground than if you simply dropped him from that height.