I think there's clearly a difference in perception between crying as a show of strength vs weakness. My intuition is that it's strong if you're crying after "coming back from the battlefield", after a long buildup period of stoicism and having given a fight all you've got, and weak if you're crying as a matter of constantly giving into whatever you're feeling in the moment. The examples in your link are as far on the "strong" end of the spectrum as they could be.

It would falsify this if you found examples of our culture supporting guys just going through their daily lives and crying as an accessible reaction to random things that make them feel bad, almost as a sort of banality. (I think this is the bar, since culturally we're okay with women doing this.)