I was the one that declined that flag. Yeah, the user did not read the FAQ, but that doesn't inherently make the question off-topic.
We've got a long standing reasoning here that just because something is at home does not automatically mean it's off topic (if I have time later I will find the relevant posts). Take for example:
I have CentOS 6 server at home that won't upgrade its version of OpenSSL, it keeps saying it's not being marked for update!
The fact that the server is at home is irrelevant to the question and the solution.
In the case of your specific flagged question, the fact that it's Windows 7 is irrelevant; the same question could apply to Server 2008 R2, which is on topic. It might even apply to a Linux server.
It would not be appropriate to make these edits unless you are reasonably certain that doing so is "safe" though. For example, if someone is having trouble sharing a file to 2,500 users and they're on Windows 7, then it is not safe to edit out the OS portion as this is a very relevant part of the question (as Windows 7 has an arbitrary maximum connections limit).
Should we be prioritizing helping new users to learn what is appropriate for the site, or turning off-topic questions into answerable ones?
Our priority should be getting people the help that they need to answer their questions. Nothing more, nothing less. When faced with two choices, one of which means that the walled garden stays walled, and another one which means we break a small part of the wall but someone gets their answer, I will choose the one where we help someone. So if a question can be edited to make it on topic, without invalidating the question itself (which often requires at least some knowledge about the things being asked about) then you should do so*.
When questions are "turned around", shouldn't we leave a footnote in the comments to address the original problem?
Yes, and no. I'm personally not going to waste any more effort than I have to. I sort of think of edits as a magical fairy that comes and fixes mistakes in your homework - after all that's part of what makes the community here so unique. First time this happens, I'll just edit it and move on. 2nd time, I will edit it and leave a comment. Third time? Well chances are by then they'll either be gone, or have done so much other poor interaction on the site that their account is automatically flagged for moderator investigation and suspended or at least fired an official warning shot.
* It's worth noting that this is my personal opinion and what I do personally. There are others that disagree with this approach, and some people have left the community because of this "lowering of the bar". I totally respect their point of view, and in fact I even sympathise with it to a certain extent. However this site pretty much runs itself and mods don't really have to do too much work given the ratio of activity:flags so how certain things get actioned ultimately depends on who sees it first.