"He requested that I not only remove the archive from Dropbox but delete my posts on Hacker News, which at that point included the fake DMCA takedown."

What you tried to do there is censor and resorted to fake legal repercussions. You can brush it aside saying that it was a mistake but it is still uncool for a corporation to do that to an individual.

I see. So the comment on the razorfast.com site:

I forked Dropship, just in case, and my GitHub repo of it was deleted. I was not notified of this. NOT happy with DropBox, and ESPECIALLY not happy with GitHub.

Is perhaps not accurate then.

Since the original dropship repo mentioned on razorfast is still available (and has a pull request waiting), and the comment didn't really contain any context, I wouldn't give it much weight yet.

I'm pretty sure sending fake DMCA requests is illegal, and it doesn't matter if it's a mistake.

It's illegal only if it was intentional. A mistakenly sent DMCA request is okay, as long as the sender follows up with a disregard notice.

but what he's saying is he sent a notice of a DMCA takedown, not an actual takedown request.

Was it?

There were no takedown requests. The whole discussion is moot.