According to Stack Exchange Team (email communication), moderators are not allowed to interfere with issues they are involved in. I believe this includes declining "flags about their own behaviour" as you mention in your question:
However, I do think there is a problem with a moderator using their privileged position to influence a conflict they are ...
I changed the wording now in that comment. While I don't have a big issue with this particular case, we generally try to use neutral language here.
I handled the original flag, but I must have misread it, probably looking at the wrong comment.
No references is not mutually exclusive with VLQ. It can have no references and be quite good (albeit this would not be an acceptable answer here!), it can have references and be quite bad.
I would say use your intuition and use whichever is most appropriate on a case-by-case basis.
Technically, mods are "allowed" to dismiss any flag, in the sense that the system allows them to.
Practically, it depends on the flag and it might not be the right thing to do at all.
If the flag is generic and not really pertinent or clear, we generally dismiss them. This is not to hide anything, or avoid a second look. It's because more input is needed ...
The flag handling dialog looks like this
I think that explains the intent of moderators, they give feedback based on that guidance.
Regarding why do not see the actions you'd expect, there might be times where the appropriate action is not what you'd expect. Sometimes, the appropriate action is... waiting it out. Other times there might be conflicting ...
I see two questions here.
What is the "effect" of a Helpful flag?
I'm going to be a bit vague here, because I am not sure.
It used to be incorporated into a "Flag Weight". That figure is no longer displayed. I am unsure whether it still used behind the scenes.
It believe it was used to try to filter out people who flagged inappropriately. I assume Stack ...