I'm the author of the article.
The 3560G/E/X series has a "funny" way of doing TDR. You are correct, the output you've posted should've mean that the AP shouldn't be getting PoE ... Unless you're looking at the wrong port (can you post the output to the command "sh power inline") or the AP is getting power from a power injector or power adapter.
In regards to the "length" issue, this boils down to the hardware (of the switch), the "quality" of the cable and the IOS. I have seen results like these on 3560 switches. When I move the cables over to 3750G/E/X or 2960G/S the results were totally different. Another thing to consider is the quality of the cable. Really, really bad quality cable, regardless of switch model, will also contribute to a reading with different length values.
Another thing, what is the model of the AP and is this AP have a GigabitEthernet interface? If the AP is capable of GigabitEthernet then it probably makes sense that the negotiated speed is only 100 Mbps instead of 1 Gbps.