Not a true statement, the hue and saturation of the colors in your image are affectd
by the ambient light around it in the same room-including the tungsten (3200K) modeling lights in your flash. If you are daylight balanced to your flash, and have a long exposure with strong modeling lamps, they will add "warmth" to your image hues and saturation in your subject. But that would take some longer shutter speeds than 1/60 of a second at ISO 100.
If you have a four-walled studio with no windows and no other light influence, for most speeds the color of the subject will not change as the flash is your shutter speed for your camera. Throw in some ambient light, the flash is still your main shutter speed, but the shutter speed of the camera may allow other light to influence the end result if it's slow--only with ambient light in the room. That's also a technique called "dragging the shutter" and this image is a great example of dragging the shutter to change the color of the skies (background)
Thanks, rg sends!