Olbers' paradox: why is the night sky dark?

http://en.wikipedia.org/wiki/Olbers%27_paradox

I think treatment originally used to discard inverse square law as the solution to this question was not set up correctly. I would like to confirm my findings, but people working in Astronomy and Cosmology field are not receptive to even discuss it as it seems that would somehow contradict mainstream theory, which is what brings me here. So this is what I think about it, please let me know if you see any mistakes:

The original treatment ignores sensor surface area, that is some 2-dimensional image receiving this light, like a photo or human eyes, and by ignoring that they get result as if the image has only one pixel. So instead of to "see" many dots, some bright some less bright, they practically sum all the received intensity in only one pixel and thus result wrongly indicates the sky would be bright. They also ignore exposure time. The rate of incoming photons is proportional to distance, due to inverse square law, which I find is well documented and accepted fact, and just by looking at that makes it clear to me inverse square law explains it all.

Let me explain with an example (all the stars are the same). Two stars at distance r would impact photo-plate with intensity I, and eight stars at double the distance will also impact photo-plate with the same intensity I. That's what they are saying, and that's fine. However, what they are not considering is that two closer stars will produce two dots each with brightens proportional to I/2, but eight further stars will produce eight dots each with brightness proportional to I/8.

There is difference between two bright dots and eight less bright dots, and there is difference between two dots on 10x10 resolution image and 1x1 resolution image. So when they ignore this sensor surface area they practically work with 1x1 resolution image where all the intensity gets summed up at one pixel, and all they see is "bright sky". To summarize I draw this conclusion: at infinite distance there will be infinite number of stars and if we had infinite resolution they would produce infinite number of dots, but the brightness of each dot would be I/infinity, which is pretty much nothing but black.