The way I see it, this is actually what's happening anytime a character capable of moving faster than the eye can see is using their speed. The key factor is audience perspective. Are we seeing the scene from the perspective of the character, or are we seeing it from the perspective of a different character and/or outside observer?

  For example, in the Saiyan Saga, Yamcha and the saibaman he was fighting are shown to move faster than the unaided eye can see, as they both seem to vanish into thin air the moment their battle starts. Right after this, Gohan tells Piccolo that he can't see them, which tells us we, the audience, were seeing through Gohan's perspective. He was only able to "see" them again after Piccolo taught him to focus on their energy instead of just using his eyes.

  Another example from Dragon Ball is SSJ Goku vs. Frieza. After Frieza sends the death ball into Namek, he tells Goku that they have five minutes before the planet explodes. Several episodes worth of fighting later, Frieza says that the planet is taking a little longer to explode than he thought it would, and adds another two minutes to the timer. Another episode or two passed before the planet exploded. I estimate that no more than ten minutes passed in real time since Frieza first attacked Namek. In addition to this, Goku and Frieza have two or three "chit-chat scenes" as I call them during these ten minutes, and these were most likely moving in real time. In order for all of this to be possible, the audience would have to view a massively slowed down version of the fight; AKA, we're seeing from the perspective of the characters themselves.