Same here...as part of our building/deploy process, and as part of our "tune-up" process, we always update the BIOS. I've been going this gig for over 25 years, including back when working at the big Computerland chain. I probably am not kidding when I say I've probably done near or over 10,000 bios flashes. I've had 1....ONE....bios flash gone bad. And that was a custom tweaked 3rd party BIOS flash on one of my own Asus gaming rigs that already had a prior custom flash on it. Re-worded..THAT was a high risk system. All over ~10,000 or whatever BIOS flashes...gone good. HP, Dell, Lenovo...done thousands of each. Sitting right here in this server room at a Hospice agency right now...doing 3x laptops right now, 2x Dells and a Lenovo..and along with the driver updates, doing BIOS flashes.
As for the OP, no, Microsoft does not do BIOS flashes with Microsoft updates. Microsoft is concerned with software, their operating system, and system drivers. They would not take on the liability of forcing a BIOS flash on un-trained residential end users. (since you have to be careful when doing one, don't interrupt it, don't disconnect power, etc etc).
Either your end users told you some baloney story, or...it was a manufacturer utility that was set on "auto update"....which did the BIOS along with drivers and some essential Windows updates necessary for the drivers and other system software. For example, Lenovos ThinkVantage tools can be set to automatically run. Guessing HP may have a version out there..I'm not sure, don't work on a lot of HPs anymore...I've mostly gone Lenovo.