At least for my generation of male Americans, I grew up in an atmosphere of childhood/adolescent homophobia. I think every generation of American men is raised with this obsolete focus on fitting into a "rugged man" archetype. I say obsolete because we aren't frontiersmen anymore and farmers don't have to fight off native attack parties or local brigands to protect their family and livelihood. Now fathers have to come up with excuses for why you have to "be a man," and devise their own definitions of that concept, because they certainly don't know either. If they don't have a good explanation for it, then they don't raise a son by instilling values of "manhood" into them, but they instead bully their child for displaying attributes or habits they feel go against it. Well by the 90's, adults have become aware of homosexuality and this "new" sensation begets homophobia, and fathers have an easier target to bully their sons into not being besides, "a weakling" (because now child has to define weakling) or "a girl" (because as a child I know my behavior doesn't determine my gender but I feel bad anyway because you are telling me for some reason being a girl is bad and that I am bad for sharing qualities with one. And this latter point I think explains the base, sexist tendencies for boys growing up, but that's a whole other rant.) However, you can't tell if a person is gay unless they tell you they are gay, and growing up in this atmosphere means being gay is "wrong" or "bad," so of course a gay child has to hide it, and bullies know that. Bullies will pick on any "gay" behavior anyone exhibits as they were raised to, and then accuse that person of being gay, which means one less person to threaten their own self-assuredness.
America is already pretty conservative when it comes to nudity, so there is already reason to not be naked with other people. Being naked is a big deal and people are uncomfortable seeing another person naked. Now we also have boys being told that it is bad to like boys if you are a boy, and boys who like boys want to see each other naked or like dicks or yada yada. So now there's two reasons to not be naked with other boys. How about a third? The penis. Don't need to say much else we've talked it to death: grow up in a size matters society, we seem to super care about what a penis looks like but we have no idea what anyone's penis looks like besides in porn, "is my penis normal? what if I'm different and everyone laughs at me" because a kid doesn't understand everyone is thinking the same thing. You get the picture. So at this point you have to have a really good excuse to be getting naked with other men. You can change in the locker room without taking your underwear off and you don't have to shower because you can just do that at home. When you get older you smell more when you sweat and you have to attract girls you are a teenage boy now, so you will risk showering, and if you are on a sports team you will all shower together -- and this is where my knowledge ends because I've never been on a sports team or showered with other men. I hear men also shower at public gyms but am willing to bet most young guys will do what they can to cover up in those situations and not talk to anyone behaving otherwise. Americans think it is "weird" to expose oneself unless it is absolutely necessary: "Oh my god put that thing away, that's so nasty to breastfeed your hungry baby, there's acceptably inferior bottles for that you pervert!"
Any way my points is, I have been friends with my group of best male friends for over a decade and we haven't seen each other naked and it makes me sad. Any expressed desire to would be responded with, "Why do you want to see all our dicks? That's weird."
Judging by the video and from personal experience there may be many similarities with a woman's perspective on same-sex nudity but there is an obvious jump in discomfort for men in general.