Low Pass Filter - pixel correlation
Most images are inherently low-pass: the object that is displayed in the image generally doesn't change from pixel to pixel.

Most image pixel noise is generated by each individual pixel capturing the image. As a result this noise is generally assumed to be uncorrelated from pixel to pixel.  That means the noise is  (bandlimited) white noise, which has uniform components across all frequencies low to high.

So, when you apply a low pass filter to an image, most of the information about the objects imaged will pass straight through because they are in the low pass filter's pass band.  

Conversely, noise will have its high frequency components attenuated by the low pass filter.

That is why the statement low pass filters effect noise more than the real data is generally true.

To answer your explicit question:


  Does this mean that the filter effects noise more due to the noise being correlated from pixel to pixel?


The filter affects the noise more due to the noise being uncorrelated from pixel to pixel.