The video, and many of the other single-stair advocates I've encountered, are frankly a bit glib about the issue. First off, the benefits (cross-ventilation and so on) of single-stair, point access designs are achievable under the two-stair constraint (see the
'Fab 'Plex for an example of a two-stair, two-point access apartment building).
Second, and more importantly, even in the case where single-stair reform is considered desirable enough to pursue wholeheartedly, the zoning-reform-like approach single-stair advocates seem to be taking to the problem is wholly inappropriate for pitching a change to the core egress requirements of the building and life safety codes. What they need to be doing instead in order to get the fire folks to sign off is doing their engineering homework in the form of fire modeling and validation/testing, or at the very least finding detailed safety cases from countries that do support taller single-stair buildings.