Do an experiment at home:

Put rollerblades on your brother.
Put him on a treadmill at any speed. Notice how (if the wheels are truly free-rolling) he doesn't move? Forward or backward, he doesn't move at all?

Now increase the treadmill's speed. He's still not moving. The wheels on the rollerblades are spinning wildly, freely, faster and faster, but he doesn't move.

Leave him like that for a few minutes. Get a sense for how all that energy from the treadmill is wasted on those free-rolling wheels.

Now, walk up to him while the treadmill and the rollerblade wheels are still spinning away. Push him in the back (maintain the push, just like a plane would maintain thrust!), and watch him roll forward into the treadmill's control panel.

Why?

Because the treadmill acts on the roller-blade wheels ONLY. The exact same way the treadmill will act on the free-rolling landing gear of an aircraft.

Your push acts on your brother's body the exact same way thrust from an aircraft's engines works on an airframe and the attached wings.

The energy being used and delivered at the wheels while on a treadmill simply has zero impact on the airframe.