It isn't a question of age. It's a question of being a supercilious, insensitive knobend. And I speak as one who doesn't like bringing personal issues to the workplace or talking about myself in that environment.
Assuming the authority to speak on others' behalf would be too much even from a Line Manager. The only exception is in the very specific circumstances of Bereaved Colleague proving so disruptive an influence on productivity that others had complained, or that work flow was being seriously affected. And in this case, were I LM I'd be having a quiet word with Bereaved Colleague about taking some compassionate leave and getting support to deal with her grief.
To any other colleague, this is not their place. If you don't like it, the correct thing to do is get the hell on with your own job, and if you don't want to listen to them talk about their circumstances, tell them so.
Other people can draw their own boundaries if necessary. This isn't in other colleagues' remit. Supercilious Colleague has stepped far out of line, and again, were I LM, he would be spoken to quietly about basic respect for others.
People like Supercilious Colleague are usually the first to demand consideration for their own mental health. Unfortunately, if all workplaces were to adopt his own unofficial policy, he'd be very unlikely to get it. Doesn't hurt to bear in mind that one day, the person in need could be us.