HDRi rendering will always impart a tint from its ambient illumination and, depending on the type of image, it can oversaturate the scene with a prominent hue.  Although many users would prefer to only use HDRi lighting as the main source, I have come across literature that recommends using such lighting as a supplement to additional scene lighting.  I feel that it is better to take a cinematographic or photographic approach to compose a well-lit scene than to rely on just one lighting style or technique.  Granted, you might want to emulate a particular, realistic style like a sunny, midafternoon day, but when you try to show as much detail at both ends of the spectrum without enhancement, you compromise for something that you are not too thrilled about.