Working in HR, I've seen senior managers shed tears. No one is immune.
A lady at work was seeing a man at work. He broke up with her. She cried openly at her desk, in the kitchen, in her colleagues office, everywhere, to everyone, anyone that would listen for about 1 week. A few complaints were made. Her work suffered terribly.
That was an unpleasant conversation. Referring her to employee assistance program etc... It ended in tears. It didn't help that her ex then hooked up with her much older counterpart (facepalm!) shortly afterwards!
This was quite extreme behaviour on her part, we tried to ensure she got the right help, I felt awful for her.
In saying that I do think crying at work is perfectly fine, we are only human after all.