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If only this was posted earlier, we could have saved 40 pages of reading!
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The last 30 pages didn't deal with the fact that you couldn't take off, but with the fact that the OP worded it wrong, and is now trying to support it by saying that, "oh yeah it works as you approach infinity." If Sklansky pulls himself forward the wheels on his skates are moving at a different speed than the treadmill, so actually, you are proving the OP's conditions wrong with this picture. If sklansky merely hold's on, sure the speed of the wheels and conveyer belt are the same, but his speed relative to the ground (read airspeed) is 0, thus no lift, thus no takeoff.
Edit: Nice Picture though.
Edit Edit: I have now surpassed my quota of OOT posts for the year, so I'll leave this topic be. Its clear that the other side will not admit that they worded the problem wrong, and this is pointless.
Edit Edit Edit: And if the fact that he's facing against with the treadmill is meant to imply that the plane could be travelling with the treadmill, well thats not the way the OP was worded.