No, I think the DUmmie is saying that the two of them had uncontrollable nervous laughter, which does not mean they thought it was funny. Doesn't actually say they didn't think it was funny, either, but doesn't give any reason to believe they were glad he was dead either). Some poorly-adjusted people do react to stressful depressing situations this way.
The bigger point the OP is trying to make is that people will take the news in many different ways, and is asking them not to get wound up jumping on each other about what their reactions 'Should' be. If it had been more clearly and completely written, it could have been a 'Best of' post.
I thought pretty much the same thing.
When it's a close family member who dies, those left behind, have had a very exhausting couple of days, if not weeks, months, years. I can see where something "odd" happening, could make one giggle, and if one is totally exhausted, the giggle can turn into something that is not really funny, but bordering on tears. It's more of a hysterical reaction, rather than a Ha-Ha funny reaction.
Mourners are also going to react differently at the funeral of someone who has lived a long and full life as opposed to one who's life was cut short either by illness or by tragedy.