It's not about the content of the joke usually, it's about context. Make a joke about cancer at a comedy club or down the bar with friends, fine, make it in the children's cancer ward of a hospital or at a funeral, you're just being an asshole.
That one the OP mentioned, it was pretty poor, a thread like that I consider to be similar to a eulogy, of a kind, a report of a death oughta be fairly respectful.
After all, even if you didn't like the person, they had friends and family, and unless they deserve the mocking, like Hitler, Gary Glitter, Fred Phelps, etc., then you're not just knocking a dead guy.
A good example was when the Daily Mail (yes, he on about them again), orchestrated a massive campaign against Jimmy Carr for making a joke about amputee ex servicemen coming back from the middle east, how at least we'd have a great Paralympic team in 2012.
Now, he's told that joke to (and if we're honest, maybe even got told it by) the very people he's talking about, and it was at a charity benefit gig for soldiers. People chose to come and see him, knowing what he's like and what kind of material he does.
The Daily Mail then reprints the joke, all outraged, thusly telling the joke to millions of people who'd never go to a Jimmy Carr gig because they don't want to hear that kind of humour.
How on earth is Carr the bad guy and the Mail the hero of good taste?
In short, any joke is fine, if you consider the audience, both at the time and who'll hear/read it later on. Hell most comedians adapt their material to suit their audience, if they're in a military heavy city, they'll probably do more war material, if they're in a middle class area, more chav material.