I don't really agree with that in modern day Europe. The media companies don't toe the government line more than you'd expect in any country with a free press. There are often concerns about the closeness of ties between politicians and media but I think that's pretty common in Western countries. Moreover, in the UK the government itself makes a big deal of how important our relationship with the US is. Besides that, I'd argue that you're underestimating the reach of both the Internet and US culture generally. The Internet makes it easy to get access to a wide range of news sources, at least for those who are motivated to do it.
Probably more importantly, I'd guess that easily half the popular TV and most of the movies in Europe (and probably much of the world) comes from the US - there's a lot of information about US culture, self-image, even simple turns of phrase that continuously percolates into everyone's minds from this alone. People continually get (arguably idealised, since this is Hollywood) images of what the US stands for, what it's like to be American, etc. In terms of the vast entertainment industry, I'd argue that Europeans are routinely shown the same image of the US that Americans themselves receive.