Okok here's an analogy, not sure if this will work for you.
You got two cups. One with 5cm diameter and one with 10cm diameter, both have the same depth. Put both in a down pour and see which will collect more water at the same period of time.
A larger sensor vs a smaller sensor of the same pixel count, means the size of each pixel is different. If each pixel is like a cup, then a larger pixel will "collect" more light than the smaller pixel at the same given time.
You kept arguing that they will receive the same amount of light if the light source is the same. However it seems that you are quantifying the light by the number of photons that YOU ALLOW to hit the pixels, which is unrealistic. In the real world, the amount of light is controlled by the aperture and shutter open time, which means at the same given time, there will definitely be more photons hitting on a larger pixel than the small one.
Another way to look at it is, take the D700 sensor and turn it to DX mode(6mp). Its noise performance at DX mode will be the same as FX, which is better than D90 which has a 12mp DX sensor.