That's not the reason. Sony and Microsoft wanted x86-APUs for their home consoles. Nvidia is not allowed to make x86-CPUs or x86-APUs because they have no x86-license.

Nintendo obviously wants efficient ARM-based mobile SoCs for their console. Nvidia can offer that.

Nvidia

If its a hybrid or home console > AMD
If its a portable with a HDMI-out and a docking station (not really a hybrid) > Nvidia

Nintendo talked about plan for unifed platform and having same artecture, so going with Nvidia on one deavice and with AMD on other devaice is totaly again such a plan and make any sense.

Eurogamer article talk about handheld and base unit that basically make handheld home console in same time, so NX is a hybrid, not just handheld or just a home console.

Yes it is.

Not just that, but first info we had about Nvidia on NX (SemiAccurate) was telling that Nvidia gave Nintendo very good deal. Here is that info from May.

• Though Nvidia downplayed console margins, their pride was hurt by the loss in console contracts. All the talk about "focusing on Shield" was a cover for the fact that MS and Sony had soured on them and would not enter negotiations.
• Nvidia team was told to get a console win or "go home." Enter Nintendo, who apparently made off very well in this deal. This to the point that SemiAccurate questions whether this is a "win" at all for Nvidia.
• SA has heard that Nvidia are promising software, support, and the whole shebang at a very low cost. According to one source, Nvidia may even be taking a loss on this deal.
• Not mentioned which generation of Tegra or process node will be used or when the handheld is scheduled for release.
• No mention of the home console, but we can speculate what that might be and who might provide the chipset for that one.

http://semiaccurate.com/2016/05/12/guess-whos-silicon-is-in-nintendos-nx/

Nintendo's technology higher ups also have ties to Nvidia.

Nintendo's current head of System Architecture and head of their Hardware Technology Department is a former Nvidia employee

https://www.linkedin.com/in/ssudharsanan

Nintendo's Senior Graphics Engineer as of July 2016 previously worked at Microsoft and not Nvidia per se, but guess which SoC he worked with while at Microsoft?

https://www.linkedin.com/in/joshua-buckman-7331a953

The Nvidia Tegra. 

" I also did UI and rendering technology evaluations on the NVidia Tegra SOC."

So likely "switching" to Nvidia was not very hard for Nintendo. Their Head of their Technology Department is a former Nvidia employee who would know the company well, they have a senior graphics engineer who has worked with the Nvidia Tegra SOC.

Its gonna be AMD. Nvidia themselves said they are focusing on smart cars. There was no wins announced and AMD already announced design wins.

Its time to give it up. Unless Nvidia is not telling their investors everything then NX isn't happening.

Neither AMD nor Nvidia will "provide silicon for the NX" because they don't have foundries

I'd be willing to believe it was Nvidia if it wasn't for this.

Nvidia doesn't downplay console margins just for the sake of downplaying them.The truth is that console deals would be negligible for a company as successful as Nvidia unless of course, they were on the winning end of the deal which this guess implies otherwise.In case you don't believe console deals even one that benefit both parties are negligible just take a look at AMD, they currently manufacture for all consoles yet they are in the shitter.Why would Nvidia want such deals? and even more so why would they want a losing deal?

I believe the Tegra X1 rumor.
Because it makes sense if the idea is to have a cheap tablet handheld, that you can hook up to your tv.

You d want a mobile chip for a device like that, the fact that it uses like 20watts of power? no biggie, they just downclock it when your holding it (and you play at lower resolutions), and go full speed when its in its docking station (and your playing on your tv).

You're missing the point.

Now you get closer!

The three main reasons why poeple is saying AMD are tradition, hope and economy

1-Tradition. Nintendo has always used AMD GPUs, and some want to see that relation keep going.

2-Hope. With the PS4 and X1 featuring AMD GPUs, some poeple hope that, if Nintendo has an AMD GPU, ports will be easier to make, and the chances of getting more third party support will increase. Poor fools.

3-Economy. This ties with the sentence I underlined. Nvidia has indeed more powerful GPUs, but they are also more expensive. That means that, for the same price that you can get a Nvidia GPU with X power, you can get an AMD GPU that's more powerful, or one with the same power but at a lower cost.

Also, yes, AMD could be using the Tegra X1 as a placeholder. The X1 features standard A57 and A53 cores that AMD can provide since they have an ARM license and their K12 chip is based on the A57 models. The GPU part is a bit tricky, but Nintendo's middleware could take care of that.

That could also explain, at least in part, the delay, as the K12 was delayed to 2017.