Things are more complicated than the way shown in this video. The letter s is pronounced the way that video shows only in Northern Italy (the woman and the boy are from Northern Italy). In Central and Southern Italy, things are different. In Southern Italy every s is pronounced [s], except when it precedes a voiced consonant (b,d,g,l,m,n,r,v). In Tuscany, intervocalic s is pronounced sometimes [z], as in 'caso' [ka:zo] - like the english s in 'deserve' - sometimes [s], as in 'casa' [ka:sa] - like the s in 'assignment'. The difference between s and ss is that the double s is held longer: "casa" is pronounced [ka:sa], while "cassa" is [kas:a]. Note that the vowel in open syllable is longer than in closed syllables.
In the last decades, the intervocalic s, in the so-called "doppiaggese" (the artificial language used in dubbed movies) is pronounced [z] as in Northern Italy, but outside dubbed movies, everyone follows the pronunciation of their region.
The classical Italian pronunciation of intervocalic s is, however, the pronunciation you can find in Tuscany.
Dette er nemlig Formelen, som beskriver Selvets Tilstand, naar Fortvivlelsen ganske er udryddet: i at forholde sig til sig selv, og i at ville være sig selv grunder Selvet gjennemsigtigt i den Magt, som satte det. (This is namely the formula, that describes the condition of the self, when despair is completely eradicated: by relating itself to itself, and by willing to be itself, the self is grounded transparently in the power which constituted it) (Søren Kierkegaard, The sickness unto death)