I think most Europeans know, that most places in the US are safe.

For me the difference is, that I live in the most dangerous city in Germany (statistic inflated due to giant airport) and would still walk through every street here at any time. I do not think that I would do the same in some parts of LA. So maybe my understanding of LA is a bit cartoonish - and granted you do not walk in LA anyway.

"Europeans have a cartoon understanding of the US"

Unfortunately that appears to work both ways.

I didn't visit US and I don't intend to do it soon(ever?), but I would have some "cartoonish" fears like: being detained/harassed/turned back in the airport for possible stupid/hostile remarks I made (who knows when, who knows on which forum) about US gov or foreign policy; Or being shot without witnesses or strangulated to death by some psychopath policeman because "resisted arrest" and so on..

Many of us see the USA through your "Hollywood window", media reports and statistics. Imagine how easy it is to be worried about your personal safety.

The reason I do not plan to visit is because of that image about gun-totin', mentally unstable nation out of touch with reality with bizarre and secret laws which are in the worst case enforced by trigger-happy people with less than 5 months of training. Terrifying. But you aren't actually safe from them in a different continent either: attending to a wedding in Mid East can be lethal...