I know I won't be able to convince everyone here, but I didn't feel pressured to share anything deeply personal. Some people on the team didn't. They weren't punished or looked down on. We were a tight-knit team before and after that event.
Interesting to know. Seems people who reply here, a bit assume it's a group of competitive coworkers who mostly don't know each other, in a big cut-throat corp?
I'd been ok with that meeting at my first job (together with my closest coworkers only). It'd been weird at my 2nd job though. I guess it depends :-)
(But it wouldn't have been needed at all, there. I guess that's related to why it would have been ok.)