That's clearly not the case for all the examples in the page I provided.
Even just the category itself kind of makes the point. The original claim way upthread was that women find guys who cry repulsive. I would assume this is roughly referring to guys crying when they run into a problem in life instead of dealing with it, that sort of thing. The examples in your link are, like, guys who gave their whole lives to a sport, everything's on the line, maximum skin in the game, and their crying is a show of strength, the raw emotion of someone at a peak/climactic moment.
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.)