Incorrect. While what happens after the sensor does play a role, it is all about light gathering and that is entirely done by the sensor. Why do you think the D4(s) has such massive sensor pixels? More light, better colors, less noise. It's about surface area times quantum efficiency. The reason there is no DX capable of doing what an FX does (in terms of light) is purely of a technical reason; too small sensor pixels. If they develop a lower Mpix DX tomorrow, they could increase the pixel size and gain the same light gathering as an FX but no 24Mpix will be able.
Even the D810's increase in Mpix comes at the expense of light gathering because you can't put more pixels on a surface area and maintain their size. If they develop a 50Mpix FX with exactly the same pixels as a DX it'll have the same low light performance a current DX has.
I personally would never trade light for pixels.
New technology like the BSI sensors might make the new DX outperform the current FX but since that technology can and will be applied to FX too, DX will always run behind. It simply lacks the surface area to compete. Just like no FX can ever compete against a medium format.
So the D300 should outshine the D810 in light gathering and low noise at higher ISO. No?