No question those biases exist, but it's mistaken to think that vulnerability requires confidence "not of the masculine type". There are different ways to be vulnerable. Some have to do with being willing to take risks.
Say you're in a group situation and it is affecting you in some way that's not ok—not merely annoying, but touching something of deep importance in your experience. If you bring that information into the group and state what you're experiencing, you make yourself vulnerable. That takes confidence and strength. Then it takes strength to face the effects of that action, whether in the group or from an authority. And another strength too: by speaking of what you're personally experiencing, rather than accusing others of doing something wrong in the abstract, you preempt many conflicts that would otherwise arise. That is self-responsible.
To be vulnerable in that way is very much to "support yourself instead of elaborating victimist narratives". The victim reaction would be to say nothing, feel bad, and carry a residue of resentment. That's what most of us mostly do.
Vulnerability that comes from strength does impress others. When someone shows the capacity to speak coherently from a wounded place in a situation where it is called for, the quality that fills the air is dignity. The reactions I've observed in people at moments like that are admiration and a sense their own experience was touched, as if the one who spoke had spoken for them as well.
It's important not to confuse confident vulnerability with reactions that come from unprocessed woundedness getting activated in stressful situations—"bursting into tears during a code review", as a commenter memorably put it. Those reactions may be vulnerable but they don't show vulnerability in the sense of making a conscious choice to show oneself in that moment. They are more like a buffer overflow, with emotional bytes streaming through a breach in one's facade. Uncontained reactions make a situation more complicated because they are usually "too much" for the moment—the energy in them is coming from some other place more than what's happening right now, and not under conditions that offer opportunity for healing. That tends to result in wounds getting repeated rather than integrated.
The reason it's important not to confuse those things is that if you do, you'll probably get stuck with two shitty options: (1) push your pain away even further, stiffen your facade and pretend to be what you're not; or (2) expose yourself in uncontrolled ways that show weakness and that others find unattractive. Actually, you'll probably get stuck with both: #1 as your default and #2 bursting out in stressful moments. (I don't mean "you" personally, but generally, or at any rate about traditional male roles.) An alternative is to stop pushing away pain, face what one is denying, feel it fully and allow whatever happens in response. That brings healing and strength—genuine strength that one can feel in oneself, as opposed to pretend strength that one doesn't really feel. This doesn't happen all at once; it's one piece at a time, but usually each piece provides enough relief that the process sort of 'pays' for itself as it goes.
The other thing is—much as a lot of us, me included, would prefer otherwise—it seems to need to take place in the presence of others. The value of the work described in the OP, or some of it anyway, is that many men who would never otherwise take such a step find it possible to do so in the presence of other men, when the process is organized a certain way. This is a surprising phenomenon—it surprised me anyhow—and I don't think it's widely understood, but it's a good thing to take advantage of if one feels a pull in that direction.