According to the official WordPress docs, when you save your
Permalinks it updates your .htaccess file …
This isn’t correct. When you switch from default– ?= permalinks which are nothing but pure PHP URL parameter passing– to anything else then WordPress will create a .htaccess file if it can, or tell you to create one. Once that file is created the permalinks are generated entirely internally to WordPress. The .htaccess file does not need to be, and isn’t, updated every time you change permalinks. You can see the file_exists() check in the save_mod_rewrite_rules() function.
Specifically, what happens in that WordPress creates a .htaccess file telling the Apache to send all requests to the index page thus allowing WordPress to take over.