Right, the only problem with your analogy is that no part of it made fun of suicide. It made fun of Kat. Just because suicide is involved in a joke does not mean it's making fun of suicide.
The equivalent to what you're talking about with the racist joke would be to hear a racist joke and then you turn around and say, "HEY, I'm offended by that--I had a black friend in high school." Which would sound FUCKING RIDICULOUS.