Let me try this scenario:
Take a shopping cart, a treadmill and a length of rope. Tie the rope to one end of the shopping cart, like you were pulling it behind you. Put the cart on the treadmill and turn it on with the rope slacked. The cart would be stationary, the wheels of a shopping cart do not produce and power and are there only to spin as the pusher provides thrust.
So we have a cart on a moving treadmill, just sitting there. Now take the rope and begin to pull on the cart, does the cart remain stationary? No, the wheels spin at an increased rate based on the speed you pull and the speed of the treadmill. Since the wheels do not factor into how fast a shopping cart moves, the cart moves forward with an increased wheel speed.
Now, double/triple/quadruple the speed of the shopping cart as you are still pulling on the rope. Does the increased speed stop you from being able to pull the shopping cart forward? No, once again, the wheels spin faster and faster, (I'm assuming for this that the wheels won't fall apart), but no matter how fast they spin the cart will only move forward equal to the amount of force you are pulling the rope.
Now, if we replace the shopping cart with a plane, the plane only needs to be able to move forward to make air pass over the wings and therefore create lift. Since the plane/shopping cart will move forward how ever fast you pull it/however fast the jets propel it, the plane will take off as normal.