First of all, I am not a carpet installer or dealer...I know very little about the fuzzy stuff. However, I believe that the inspector may be right that the color difference is a visual illusion. You can easily determine if that is the case by blocking light from the window. If the illusion disappears when you do that or when you turn on the room lights, then that is your problem and not a problem with the carpet. I have experienced such illusions, only in my instances they appeared across vinyl flooring. In one instance the 'dividing line' where the light from two different light sources met fell exactly on a tile line in the flooring pattern; I could make the illusion come and go by switching one of the light sources on and off. But, it sure did look like I had installed two different runs of flooring.

Your installer got the pattern match dead on. That would be a very difficult carpet to do a perfect seam with.

I live in Seattle as well and worked for Mohawk and other carpet mills for 20 yrs. If this is a cut pile you may see a seam but mostly they should be invisible. When you put the seam tape it slightly peaks causing the lighting situration you describe. Mfctrs don't make seams so they will have liablility. Get a good installer CRI certified and get his opinion. Lots of people can install basic carpet but it requires a little more skill on high end, wools, berbers etc. I'd get another opinion, but agree with inspector.