Touching the ball to a boot is not the whole description
Law 20 requires the ball to be kicked a visible distance; a ball held in the hands must clearly leave them. The player can then play it again. That sequence explains why officials sometimes bring back a hurried attempt.
Imagine a player holding the ball against the toe without releasing it, then running. Compare a small kick that clearly leaves the hands before the ball is recovered. From a distant camera both can look like the same quick gesture.
Watch the separation before the run
The relevant close-up is the gap between hands, ball and foot, not the later metres gained. A powerful run cannot repair an earlier restart that was never taken in the required way. Conversely, a very small visible kick need not resemble a long tactical kick.
Identify the mark as well as the ball action: where the restart is taken is a separate requirement. The original comparison isolates the visible-kick condition and does not suggest every tap near an official is valid. It explains why a referee can halt momentum before the attack begins to develop, even when the scoreboard and match clock barely changed.
Questions answered
Must a quick tap travel a long distance?
No, but the required kick must be visible.
Can a later run prove the tap was correctly taken?
No. Examine the initial release and kick.
Sources & further reading
Official references for the subjects discussed. Service terms and device software can change.