TL;DR: In my opinion, you were not wrong to flag the comment.
I hear and sympathize with what the moderators are saying, but I want to share a slightly different perspective.
The party line is that it's not ♦-moderators' job to verify the correctness of an answer. I find that entirely valid.
However, I think there's another reason why flagging these kinds of answers as VLQ can be useful. Flagging as VLQ has another purpose that ♦-moderators might not be familiar with: it puts it in a low-quality review queue, which 10K users can view. Thus, flagging as VLQ is one way to bring the answer to the attention of other 10K users, who can then downvote it and vote to delete. Recall that deleting an answer requires multiple "delete" votes from 10K users.
Thus, if we want ordinary users to clean up the site, the challenge with doing that is coordination: we need a way to notify multiple 10K users about the answer, so they can take a look, see if they agree, and if they do, vote to delete. Right now, flagging as VLQ or NAA is one of the few ways to do that, and arguably the best way to do so.
So, flagging as VLQ serves two purposes: (1) to notify ♦-moderators, and (2) to notify 10K users. I can sympathize with ♦-moderators who don't want to be put in a position of being asked to judge the technical accuracy of answers and who feel this is best left up to the community. However, I think there's a case to be made for encouraging "flag-as-VLQ" in this kind of case, because it allows 10K users (regular users) to police the site -- flag-as-VLQ + the VLQ review queue is one of the best tools the community has to police this on their own, without bringing in ♦-moderators.
Therefore, in this kind of situation, there might be a case for having ♦-moderators leave the VLQ flag live and letting 10K users handle it as they see fit.
I'll also point out that the text under the VLQ flag says:
This answer has severe formatting or content problems. This answer is unlikely to be salvageable through editing, and might need to be removed.
I think that does accurately characterize this answer: the answer is unlikely to be salvageable through editing, and probably needs to be removed. Therefore, I think the VLQ flag was appropriate, and I'm not sure it should have been declined.
In your specific case, I think it would also have been reasonable to flag the answer as NAA (not an answer). The "answer" doesn't even attempt to answer the question -- it consists of disjointed statements, none of which answer the question (as you've already accurately analyzed). As an aside: Ideally, when you flag as NAA, it's helpful to leave a comment explaining why, so that when moderators or 10K users see the flag, they have some justification for why it was flagged, and also so that the user has a chance to understand why their answer was unsuitable and either edit it or do things differently in the future.
So, in this case, I personally feel like both a NAA flag and a VLQ flag are justified. To me, it feels like there are multiple reasons why this answer should be deleted: both because it doesn't attempt to answer the question, and because it has severe content problems and probably can't be salvaged through editing.
So, ultimately, I'm very sympathetic to you: I don't think you were wrong to flag the comment, and I probably would have flagged it, too, if I'd come across it.