Meh, that's a poorly written article.
1) Dropbox doesn't store/retain/use or whatever your admin password. During installation it requests it so it can inject itself with an accessibility permission (which is fairly unlimited, to be granted).
2) The fishy bit is that it circumvents the existing OSX elevation methods and instead just settles for the jugular - injecting itself far deeper in the system than it should.
Which really brings the crux of the problem. Why the f*k should a cloud files sync service require kernel extensions or inject itself as a virtual filesystem in the first instance. What the hell was wrong with the model where it had a folder, kept monitoring it and if anything changed, synced the files?
Me thinks we should ring up the BOFH and point him to a couple of product managers in Dropbox HQ. Heck, I'd sharpen the spade myself.