It's from electrical distribution where a brownout is distinct from blackout because you are delivering electricity but not as specified (e.g. voltage sag beyond agreed limits) and on simple incandescent lights the effect is they're dimmer than before.
I don't think it has any greater claim to being offensive than blackout (from electrical distribution) or whiteout (from weather reporting)
Regarding the offensiveness, I was hinting at GitHub's prior remarks for racial sensitivity: https://news.ycombinator.com/item?id=23500093 -- among the many other projects that have actively changed black/white to block/allow and other variations.
The idea is that even though you wrote a blog post, maybe sent out formal notices to users, even in some cases put up billboards or did PSAs on TV - some people won't know it applies to them, or may even mistakenly believe it doesn't apply even though it does.
The brownout is an opportunity for those people to notice. "Hey, why doesn't the Foozle work?" "I dunno. Ask on Reddit?" "Huh. Reddit says we need to use tokens, but I'm sure we... oh... did you actually update the Foozle script?" "I thought you were doing that" "D'oh".
Users who can't react immediately when things go bang will get a reprieve - for a while - when it starts working again the next day.
So that's why "blockout" isn't an appropriate description.
There's some degree of art and some science to planning these so that they're disruptive enough that humans notice something went wrong, while not being disruptive enough that they're worse than just a one shot change.
I don't want to beat a dead horse at this point, but that's basically a planned blackout. It'd be similar to a power company cutting off a residence's power for a couple hours to remind them to pay their overdue bill. I can't see that being correctly called a brownout.