No, it tells me there's a gaping hole in the rules when it comes to properly reflecting the fiction.I don't think the first quoted paragraph is true in 3E, 4e or 5e. If you were to read Gygax's description in his DMG of the combat round, and ignore the half-baked initiative stuff, it wouldn't apply there either. The melee combat round is full of "swings" and back-and-forth and so on.
The initiative count dictates the order in which actions are declared, and so those who go first have a chance to dictate the action (within the constraints set by the rules). What that means in the fiction is pretty wide-open, though.
Nothing in the 3E, 4e or 5e rules says anything about pips of initiative representing any amount of time. There are not 20 segments, of 0.3 seconds each, in the 6 second round. This is an importation from Gygax's initiative rules that has no basis in the rules text of those systems, nor the game play that they support.
EDIT: Here's sufficient proof of the point that doesn't even need to point to the broader issue of rules text - suppose three characters, A with initiative 20, B with initiative 2, and C with initiative 1. Each of A, B and C can resolve 30' of movement on their turn before the next character's movement is resolved. So are you really saying that A - the most quickly-reacting of these characters who gets to have the most influence over the shape of events (by having their actions declared and resolved first) takes 5.4 seconds to move their 30 feet (just over 5' per second), while the low-DEX B moves 30 feet in 0.3 seconds (ie a speed of 100' per second)?
The way movement rules work in 3e-4e-5e, a moving character reaches its destination on the same initiative as it left its starting point. Example: if A with init 20 moves 30 feet to within reach of opponent X, opponent X who has init 19 can melee attack A because somehow A got there in time for that init 19 to matter (and if you think foe X is acting later in the round in the fiction, explain how someone else on init 18 could kill that foe and yet it still gets its attack in). It's like combat movement is a little mini-teleport, and that's been an annoyance to me in the RAW of all editions thoguh the WotC editions somehow seem to make it more front-and-center.
Far FAR better would be to have movement take time within the round - if you start your 30' move on init 20 you'll get where you're going on, say init 10; and if you don't start your move until init 2 your move will roll over well into the next round.