The LED strip's black wire is actually marked +12v, so it might be one of the strips you would think are wired for that controller. But it most definitely does not work if you apply +12v to that wire and then ground any of the color wires.

And the controller it comes with also definitely supplies (up to) +12 on the RGB and ground on the black.

The LEDs are all wired in parallel and connecting the wires to the other end doesn't have a different effect. It's the same from either end.

It would also not be possible to make this work only be changing around some components - the polarity at the supply would also need to flip, otherwise the black wire would still continue to receive +12 since that terminal on the outputs is connected directly to the corresponding VCC terminal on the supply side.

I'm going to take some photos of the strip and controller PCB and post them up.

In the meantime, found the same controller on Alibaba:
http://okled.en.alibaba.com/product/5212..._spotlight.html