Why do people believe Emily Rogers?

Too power hungry, if Intel couldn't scaled down x86 properly, there's no way AMD would. And Intel doesn't play nice with console manufacturers.

It can, but usually it costs more, Intel could never make it's mobile/tablet efforts profitable as it had to compete with ARM on price, so it partnered with Chinese manufacturers, should be interesting to see how that plays out in the next few years.

Plus, we cannot forget how bad Intel Graphics typically are, for AMD that isn't as much of an issue, they have experience in mobile graphics. (Aka. Adreno, a play on the word Radeon.)

Intel was able to scale down it's Atom to ARM levels of power, AMD has done the same.

Intel was also able to compete with high-end ARM SoC's as well.

AMD has managed to take a Quad-Core Puma at 1.2Ghz, 128 GPU pipelines and have a TDP of 2.8w - 4.5w. Perfectly for a Tablet.
There were also energy efficiency gains when AMD moved over to Puma+ as well.

At 14 and 16nm, the power consumption would be 2x - 2.5x lower if the gains other chips have had on that process is anything to go by.

Intel's issue wasn't actually Performance or Power Consumption. - It was price and lack of design wins, although many PC OEMS backed Intel like Asus and Acer... They comprised a small % of the market.
Intel also got a design win with the Samsung Galaxy Tab 2 10.1 a few years back, but that didn't exactly set the world on fire.

I'm not even sure what I'd want from Nintendo. I guess I personally would like if they put out stronger hardware, but I'm not sure that's best for them.

I'll almost certainly be getting it one way or the other, I just hope they find some room in the market for it.

Problems with x86 low power:

More expensive

And/or not neccessarily that much better performing than ARM when uktra low power.

ARM went the low power consumption route very early, while x86 went the energy hungry but powerful route.