Ok, long story short. The video describes it perfectly.
A picture is worth a thousand words. ;)

En résumé, nothing needs to be changed.

Explanation:
I talked to a friend who still serves in tank battalion. (I really don't know, why i didn't talk to him when this fact first bothered me in ArmA 2)
Modern tanks behave like in the game.
I only have experiences with older tank types. They all used the braked differential steering type, so the just stoped the track you selected. Modern tank transmissions can drive the tank's tracks independently, needed for neutral turn. Triple differential tank steering is the name of that magic - complexity of a space shuttle... . Means, when you steer right, they are spining clockwise. Make sense regarding to combat situations, where it is more important to face the front armour towards the enemy than to park your tank.
I beg paron for confusing some of you, i was confused too.

@Gekkibi
Then i have to say, they were programmed wrong.
I just launched ArmA 2 to check the tracked vehicles there and, they behave properly.

Just one thing to add, when you steer right or left in a real tank with steering wheel nothing happens unless you hit the gas pedal. The turning when just "S" or "D" is pressed is easier and more action styled but not as it is in real life.

@Gekkibi
Yes, you are right. I had a Mod installed which corrects it, because i thought, and still think, in a military simulation the behavior of the vehicles should also be simulated, not 100% like in real life, but the steering is one of the things which should be. Esp. as a former tank driver i always steer in the wrong direction in ArmA 3. I hope the modder converts the Mod for ArmA 3.

But, it should be implemeted properly in vanilla as well and not transfer the faults from a former version.

@Gekkibi
No, in real life tracked vehicles turn counter clockwise when you drive reverse and steer right.

During my Military Service i drove Leopard 2 and M113 and had the opportunity to drive a BMP-2 as well. All 3 tanks have "steering wheels" no steering/braking-levers. The steering _IS_ like in a normal car. The steering in reverse mode in this game is wrong. When you steer, the turning axis of a tracked vehicle is the track which is slowed. Steering left, left track is slowed or stopped, steering right the right one, so you turn around this track. The other track just turns forward or backward whichever direction is set. To summarise it, the "S" or "D" button are just stopping or slow down the left or right track. I hope my explaination discribes the problem sufficiently.