Yeah I don't think tact is really something people value anymore. Just because something's true doesn't mean it needs to be said.

I've come close to saying some insensitive things just from not thinking, but luckily have always caught myself at the last second and stammered out some lame workaround.

Some insensitivity comes from a good place, sadly. The thought is that telling people to be happy or being aggressively positive will somehow make the situation better. I think that's basically one part ignorance and one part differences in personality.