Pointing out that something is a big symptom of depression is not the same as diagnosing someone with depression. And if there's a decent chance that Stabilizer is actually depressed and doesn't know it, pointing it out is useful. Jack seems to only be recommending that Stabilizer see a professional, and, internet or no, the decision of whether or not to see a professional is going to be made by non-professionals.
I think shminux was referring to
The reason you think these thoughts more when you are embarrassed or feel low-status is more likely that those things make you feel particularly bad about yourself than that you brain is trying to give you a way to improve your status.
I sometimes have thoughts of suicide. That does not mean I would ever come within a mile of committing the act of suicide. But my brain does simulate it; though I do try to always reduce such thoughts.
But what I have noticed is that 'suicide' is triggered in my mind whenever I think of some embarrassing event, real or imagined. Or an event in which I'm obviously a low-status actor. This leads me to think that suicide might be a high-status move, in the sense that its goal is to recover status after some event which caused a big drop in status. Consider the following instances when suicide is often considered: