(Somewhat) plausible hypothesis, not something to be confidently believed (which is the working interpretation of "deduction" I'm using, as stated at the beginning of the comment).
From the differing ways we treated the same two hypotheses just now I think we're disagreeing on how fine a distinction we accept between two hypotheses before we say that they're significantly different. From my perspective, apparating into the room and walking in under the cloak are functionally the same. In both cases, the purpose of leaving a charm off is to enable Q and H to walk out of the door as if they never left, and it's that which I'd say is a valid deduction. Within all the hypotheses which fit that pattern, some seem more likely than others, but perhaps none are more than plausible.
[Update: and now there's a fifth discussion thread, which you should probably use in preference to this one. Later update: and a sixth -- in the discussion section, which is where these threads are living for now on. Also: tag for HP threads in the main section, and tag for HP threads in the discussion section.]
The third discussion thread is above 500 comments now, just like the others, so it's time for a new one. Predecessors: one, two, three. For anyone who's been on Mars and doesn't know what this is about: it's Eliezer's remarkable Harry Potter fanfic.
Spoiler warning and helpful suggestion (copied from those in the earlier threads):
Spoiler Warning: this thread contains unrot13'd spoilers for Harry Potter and the Methods of Rationality up to the current chapter and for the original Harry Potter series. Please continue to use rot13 for spoilers to other works of fiction, or if you have insider knowledge of future chapters of Harry Potter and the Methods of Rationality.
A suggestion: mention at the top of your comment which chapter you're commenting on, or what chapter you're up to, so that people can understand the context of your comment even after more chapters have been posted. This can also help people avoid reading spoilers for a new chapter before they realize that there is a new chapter.