The ZIP file you reference has 2 TIFs. Both are georeferenced, although only one of them has the term "geo" in it. Looking at the TIFF image metadata shows the following, and ArcMap shows the same information.
Which image are you having problems with? And what is the projection of the data frame?
Your "good" capture didn't come through as an attachment so I am not clear on what you are expecting to see.
When it comes to discrete raster data, especially color maps, I have always thought ArcMap's rendering engine falls short. Looking at how a section of 470012130.tif renders on my screen between Windows Photo Viewer and ArcMap.
Windows Photo Viewer:
ArcMap:
Granted, Windows Photo Viewer is treating the image as RGB while ArcMap is dealing with the color map, but it just seems the quality difference shouldn't be this pronounced.