Did you read the report you linked to?
132 % Standard Mode
122 % Movie Mode"
The color gamut is to wide on the GS4 (this makes images looks gaudy and ugly color wise). So far, OLED have consistently had horrible color and, worse, color that shifts quickly with age.
The reality is that the display on the S4 is miles ahead of what was used on the S3. You can not dispute this point. You are also correct that there is still a gap especially when it comes to solid white background where the S4 will look slightly grayish compared to an HTC One or and iPhone. But the reality is unlike a TV where people would really notice these things especially if they are watching a 2-hr blu-ray movie , on a phone you really are less likely to notice or care. The colors may not be "true" but they are bright and you just don't hear many people complaining about the colors or the display. In fact you hear the opposite and they say the display is so much nicer and brighter than their previous phones and they love the display. For color purists this might be an unimaginable horror but the reality is the general public do not notice or care about such things. There is still a gap but it has closed to the point that most people don't care and are very satisfied. If color were truly that important then people would be buying more monitors from companies like iiyama or Apple instead of Dell and Acer. Professionals that rely on color accuracy care and buy those monitors but the public is quite content with their $275 Acer LED monitor. The S4 has a display that is not only "good enough" it is better than anything they have owned before.