Iwas just about to post this as well.

If you put the bike on the treadmill, tied a role to the wall in front of the bike, then turn the treadmill on, it would not matter how fast the treadmill was turning you could still pull the bike forward. The force you use to pull it forward would only be slightly greater than if the treadmill was not running. The only extra force required is the fiction force from your wheel bearings.

The airplane example is the same thing only the force it uses is pushing against air, not pulling a rope.