I really hate the discourse around this stuff. Like, yes, disguising murder as suicide is a thing and obviously three-letters agencies do it.
But someone saying publicly they're not suicidal gives you close to zero information. People with suicidal ideation almost never advertise it publicly because, one, there is a heavy amount of social stigma attached to it, and two, publicly declaring you're suicidal is a good way to get involuntarily committed to a mental health institution.
I see a ton of jokes on social media that go "remember, X is not suicidal". How the fuck would you know? This discourse is so disrespectful to people struggling with suicidal thoughts.
If someone is struggling with suicidal thoughts and is publicly lying about it, they shall not have my respect anyway: I'm ok with being disrespectful to them.
Then, you know, bringing up suicide and it being a warning sign they're about to? The odds have shifted a bit.