It doesn't actually show that at all - which is why cricket isn't a great example to compare with. What you see on screen is the representation of an algorithm that shows with varying degrees of certainty the probability of the path of the ball. It is NEVER showing the ball "clipping the leg stump" as the commentators would have it, it is showing a low probability of impact, and it would be far more honest to instead have concentric circles around the representation of the ball to show the degree of confidence in the probability of the path taken.
That's why you have the "umpire's call" rule - because the predictive element is not certain, not least because for any given ball you don't know how many of the data points were captured. In one instance it might be a high probability the tracking and prediction is correct, in another, it might not be.
However, this is far too complex for TV display, which is why they go with what is shown, and why the commentators fundamentally misunderstand the operation of the system. The problem then is that because of the nature of it, the DRS is deemed to be correct, and because it is deemed to be correct it is followed even when it isn't correct. It's likely more accurate than the human eye, but it does make some odd predictions, and as it is the final arbiter, those odd predictions are still followed even if it doesn't look right.
Carry on with the discussion though - but cricket really isn't a good example for a whole host of reasons.