I agree that violence in fiction stays fiction, while with nudity the person is actually naked. But if I can jump in as a French person...
The main thing, from my point of view, isn't so much the "Americans are afraid of sex" (although there is a bit of that, I'll get to it later) but more the "Americans think nudity equals sex".

Throughout my life, I have seen many movies with nudity, including full frontal male nudity, in movies rated for all audiences. The context wasn't sexual in the least and there was no problem. It wasn't inappropriate. But in North America (Canada is the same as the US), seeing, say, breasts, "means" sex for people. And that's something I can't wrap my head around.
I have seen my parents and brothers naked, taken baths with them, and not worried about it. It didn't mess me up and it wasn't sexual at all. The only thing it gave me was a basic understanding of how boys look different than girls, and adults than children.

Then in art class, we drew from naked people (male and female, although mostly female. Not that many male nude models apparently) and some of us were still minors, and people weren't offended or anything. The only incident I remember is when one of the models was wearing a tampon and one of the boys giggled. Then someone else said "grow up" and it was over.

In American media, I keep seeing scenes of "ugh, nobody needs to see that" when a man is naked from the waist down, with every other character (male or female) averting their eyes in disgust (which seriously, what kind of self image do people get when they're told that?) or, for females, nudity turning you into some kind of sexual object. I don't think it's a healthy attitude towards nudity.

So I would say that's one big thing. In France (and I assume some other parts of Europe), nudity doesn't imply sex more than it implies taking a bath or not having put clothes on yet after waking up, and it's not seen as dirty and ugly, either.

The second part, that I said I'd come back to. Another worry is the rejection of sex and our bodies as something dirty and bad. That is, the US seems, from my outsider point of view, to just say things like "sex is bad, don't do it". It's a bit like abstinence education doesn't stop people from having sex, only from doing it in a responsible way.
I looked for ages of first sexual experience online to see if your theory that people are more likely to do it if they see it was true, and found a bunch of results, none of which showed a significant difference between the US and Europe, and the difference usually being the other way around (that is, sex happens earlier in the US, but it's by like 6 months so I don't think it's that relevant).
Now, do people do it more often (rather than earlier) if they see it? Quite possibly, if I see a romance movie I'm likely to snuggle with my boyfriend and make love, but I hardly see that as a bad thing. Will I go out and have sex with the first person I find? Not likely.

I think it's important to show sex as that healthy thing people do. It's an intimate form of communication, like hugs are, except of course more intimate. Yes, there are health risks tied to doing it: let's be aware of them. Let's learn about birth control. Let's learn about masturbation. Let's learn about protection from STDs and STIs, which include so much more than HIV. Let's learn to get regular check-ups.
That something is risky doesn't generally prevent people from doing it. Driving is risky, people learn to do it safely. You should learn to have sex safely too, since you're very likely to do it either way.
Not to mention the health benefits of having sex. It's not always risky, and doing it responsibly is good for you.

It's not like people aren't aware of sex just because the scene is skipped. And since they're aware of it, they can find it if they want.
Sex being something natural that is likely to happen, I feel the best course of action is to prepare people so they can know how to react to it, and how it's supposed to happen, etc. The more you hide it, the more they have to figure it out all on their own, and the more stupid mistakes they're likely to make.

As for violence in the media, I think the problem isn't necessarily the violence itself, but how much it's glamorized. You constantly see men characters particularly who are "awesome" and "badass" and "cool" because they're violent, and I don't think it's very healthy either, because it seems to me that it detracts from all the qualities that do make someone badass, and while people might not emulate the violence itself, they might emulate the tough guise (to reuse the phrase from the documentary of the same name - awesome documentary by the way).

Not to mention, the US doesn't only have fake violence in its media. It has plenty of real violence being reported on TV, much moreso than I ever saw from the news in France (from local news I mean. Obviously international news is the same).

So, here you go, this is my point of view on the subject. I thought input from someone European might be instructive (plus, it's from the country of nude beaches and nude towns!).