That gets some key details wrong; even though designed to supersede the M113, the MICV was
always about a combat vehicle, not a personnel carrier.
The original concept was that fighting in a post-NBC world meant infantry would have to fight from inside a sealed area. This means the firing ports were part of the earliest designs, not added as a suggestion during the Nixon administration.
I should also note that several the very early prototypes were amphibious; I think this was mostly scratched (timeline wise) by the point where it is joked about being added in the film.
The added scout role is true, and coincides with cancellation of the ARSV, and did follow somewhat along the logic of the movie (roughly we need a fast, armored vehicle, this is a fast, armored vehicle).
Though it predates the unveiling of it, the MICV only got serious funding because of the Soviet BMP-1. The BMP-1 was used in combat before the Bradley was out of prototype stage, and had enough deficiencies that the BMP-2 was made, and the designers of the Bradley prototypes also reacted to it.
A lot of the changes were made because the development of it was slow enough (partly due to it often not being a priority) that the vision of what battlefield it would appear on changed.