People in the public eye say stupid and insensitive things without thinking sometimes and unfortunately for them it goes viral. I wouldn't call it a sackable offence though. Some people where I work do similar things which I and others find shocking but they wouldn't get sacked for it.
Disgusting in my opinion, after all unlike people animals don't have a choice in their well being or not. These dogs couldn't escape or try to so I can see nothing at all remotely funny in anyone 'joking' about what happened to these poor animals. I could however tell you what I would do to the scum who allegedly caused the fire
The first sick joke, which I shall not repeat, though now it sounds rather tame, was after the assassination of JFK. As has been said, such jokes arise immediately after a tragedy; normally they are repeated in relative privacy but the internet has changed all that.
I don't find it 'disgusting' I just don't think it's funny. I remember years ago when the Herald of Free Enterprise sank with the loss of nearly 200 lives. There were ferry jokes doing the rounds within hours.....now that is disgusting.