That may be true of PBS, but the level of cartoon violence and gore shown by the "gang of four" (ABC, NBC, CBS and FOX) was quite high, last time I watched. It was some time ago (the 1980s to be exact), though, when my kid was into this kind of stuff. But I doubt that things changed for the better since then.
As an aside, the US teenage fascination with violence has been documented. Some time ago I had a chance to see the data from a study conducted by the UCSC comparative criminologist Dane Archer among the US and the US high school students. The subjects were given scenarios of conflicting situations (such as a picket line, or a spouse returning home and finding the other spouse with someone else in bed) and asked to write an ending to each story. The US responses usually involved some sort of gun violence, often with a description of gory details. The UK responses, otoh, usually involved verbal exchanges, but rarely acts of violence, let alone lethal.
I do not think, however, that US-ers are genetically predisposed toward violence, although such conclusion might be "supported" by the fact that the "new world" used to be a penal colony and place for exiling European misfits, and thus the gene pool of criminally predisposed elements may be higher in America than in Europe (if someone subscribed to genetic theories of criminal behavior). My own view on the issue is close to that presented in Michael Moore's flick "Bowling for Columbine" (and Barry Glassner, _The culture of fear_) - the predisposition toward various forms of violence (real and vicarious) in the US comes from fear and alienation, inflicted on the US society by the marketers as the means of promoting various products. This is an occupied country and people feel like running for their lives without quite realizing it.
Wojtek