Hi, Saneta,
I think you are correct. “…demanded that he write down…” means “…demanded him to write down…”
Your question has something to do with Subjective Mood. Like me, I also encountered so many similar sentence constructions in the King James and other Bible versions. I was so fascinated with the subjective mood that I even considered making it my subject for my thesis, but the Philippine system (I’m a Filipino) requires that all topics are (be) screened and approved for a thesis. Note that I said, ” … requires that all topics are (be) screened and approved…” not “…requires that they should be screened and approved…”). The preceding is an example of the subjunctive mood. To “require” means to make something compulsory and the equivalent word is “should”, right? In your sample sentence, the word “demand” is “to insist”, “to order”, a necessity, a compulsion— something that need be done, something that compels somebody to do something, right?. Again, the equivalent is “should”. So, why combine “demand” with “should? The most common subjunctive verbs are: request, suggest, recommend, demand, ask, wish, order, rule, require, pray, move. Wrong: I move that the nomination “should” be closed. Correct: I move that the nomination be closed. Explanation: A motion remains to be a motion (pending approval or acceptance by a body) unless it is duly seconded. A motion is only a proposal that need be seconded. A suggestion may or may not be taken, so don’t combine it with “should”. Another example, “The president was asked that he explain his huge wealth.” The president may, or may not, explain his wealth, right?
I think the new generation has the tendency to do away with the subjunctive for reasons that need not be discussed here (need not be, another subjunctive). Of course, language is dynamic–it changes. Also, I think Americans use the subjunctive more than the British people do (or is it the other way around?)
I have collected more than a hundred verb and noun words (with their usage context) used in the subjunctive from the workplace and from the Web. I can share it with you if you wish. However, I would suggest that you consult a good English grammar book for a better, exhaustive and authoritative explanation. You see, being a Filipino, mine is a Filipino English and no better than that of a native speaker.
Hope this helps.
Prax