"According to IGN, Nintendo's 3DS will skip Wii quality graphics and should boast the performance of a Playstation 3 or Xbox 360. The speculation comes from the fact that it needs enough processing power to render 3D graphics."

First, the processing power of a console has nothing to do with it's ability to display a 3D output. The Sega Master System had shutter glasses 3D and couldn't render a single polygon.
http://en.wikipedia.org/wiki/Sega_Master_System#SegaScope_3-D_Glasses

Second, we can't draw any conclusions about whether the 3DS will render each frame twice or not. Those old Magic Eye books used only a depth map to create the 3D effect:
http://www.magiceye.com/advert2.htm
Since such depth map is a standard by-product of any 3D rendering, it's possible that a clever algorithm coupled with a new screen technology can create a 3D ouput without rendering a single extra pixel.

Finally, you can't compare how the 3DS will do 3D and how the XBOX360 and PS3 do it. One will work on a 3.4 inch display, and the other must work on displays of any size, 40 or more inches...

So there you have it, this rumor is utter bullshit.

Keep in mind that what they really mean "it's as powerful at it's current res" meaning if the system displays 360x240 then then it's literally 1/4th the power of a 360, but the graphics will look just as good because there is less pixels to render.

But then factor in the fact it's going to render twice as much (for 3D) so it'll only look half as good as a 360 game.