Is it valid for a diamond moderator to use their powers to override the closing votes of other users, in order to reopen a question?

Yes, I think it's absolutely valid. We give moderators a lot of power, and the hope is that they will use that power to achieve the results they think will benefit the site the most. Generally, so long as actions are taken with the goal of improving the quality of the site, I'm fine with it.

Closing a question and reopening it immediately seems to be a perfectly valid way for a moderator to reopen a question that they think should be reopened. If the end result of these actions is to have an on-topic question be open, then I don't see any issues with it being done this way.

Yes, such actions override the actions of multiple other users. But that is just the tip of the iceberg in terms of the powers that we bestow upon moderators. They are capable of many, even more powerful actions than overriding other users' close votes. I believe they should exercise these powers in all the cases that they think is appropriate. We also trust them to be able to judge when is appropriate to use these powers.

Of course, if your question was about a specific action, then we could, and should, investigate closely whether the action was appropriate. And if the moderator abused their powers in any way whatsoever, they must be held accountable. But since you're specifically asking a generic question, I think the answer is yes: It's valid for moderators to use their powers in this fashion.

It's valid, because that's kinda what mod powers are for: doing things above and beyond what standard curators are able to do, as and where necessary.

But I share your concern in this particular case. Yes, I know this Meta question ostensibly is not about specifics, but the event that prompted it is what led to this question being asked, and without the context of that event any answers to this question are going to be brief and unsatisfying.

I was under the impression that editing a question to change the asker's meaning was verboten, regardless of whether you have a diamond or not. The asker was quite specific that they wanted a tool to do this for them, which is off-topic; if they themselves had chosen to edit the question into its current state and flagged for reopening, that would be fine.

What happened instead is that the question is entirely different from what its asker intended, and it's circumvented the standard process for reopening - both of which seem far beyond "as and where necessary".

That said, I trust our moderators. I may not like everything they do (especially when they suspend me, LOL) but I trust them. I believe that this is simply a case of lack of information (question revision history is, shall we say, "limited") and I would love to have that information made available, should the moderator in question be able and willing to do so, so that we can hopefully understand why this happened.

Is it valid for a diamond moderator to use his powers to override the closing votes of other users?

Yes, absolutely. Part of the moderator duty is to mediate in situations where several users disagree about what should be done with a post. Moderators may also use locks to prevent users from casting votes, either temporary because there is no consensus or some conflict, or permanently, because the post should be left as-is.

If moderators use normal close votes however, they don't necessarily have a final say in the matter. It is then possible for high rep (>3k) users to disagree with the moderator - if a moderator closes a post, then 3 such high rep users can re-open it. This happens now and then, when moderators make human mistakes or perhaps when they misunderstood something technical that required deeper domain knowledge.

I considered that a certain post does not comply with the SO rules since it explicitly asked if there was a tool that performs a certain specific task

Generally tool recommendations are off-topic indeed. However, there are situations where someone asks "How do I do x? Is there a tool I can use?". These can sometimes get edited into shape by removing the tool request part, if the "how do I do x" part is detailed enough. This appears to have been the case here.

Also note that posts with bounties (which this one was for a while) can't get closed by regular users, because of some site design choice. If a post with an open bounty needs to be closed, we need to flag for moderator help to do it.

The closing and reopening vote are only intended to annul the votes already given. Is that kind of action correct?

It doesn’t seem incorrect. Questions with close votes tend to attract more close votes, so a question that’s one vote away from closure stands a pretty good chance of getting there. If a moderator looks at such a question and sees either that the problem with the question has been addressed, or that the votes seem inappropriate for some other reason, then it might make sense to close and reopen the question. Basically, if a mod looks at a question and thinks that they’d reopen it if it were closed, then it makes sense to take similar action immediately instead of waiting for the closure to happen.

Moderator time is a scarce resource, so if they can solve a problem preemptively and thereby reduce the number of times they have to visit the question, that seems like a good thing.

That said, I’m confident that mods don't go looking to subvert the users. We’re all on the same team here, and the moderators rely on the community to handle most of the issues.

it explicitly asked if there was a tool that performs a certain specific task

Go back and look at the question to which you’re referring. Do you think that it should be closed in its current state? If no, then it sounds like you’re in agreement with the moderator, and the right thing happened. If yes, then there’s a mismatch between your understanding of which questions deserve to be closed and the mod’s; ask about the question in Meta to get a better understanding.

Note also that there are particular reasons for some of the “rules” about what is or isn’t acceptable. Questions like Is there a tool for X? are frowned on because that’s close to asking for a resource recommendation, and based on experience we don’t want the site to devolve into a recommendation site. But if someone is asking *whether* a tool exists, it’s probably because they have a problem, and we have lots and lots of questions of the form How can I solve problem X? So it’s often possible to convert a borderline question into a good one.