Do the Americans really have trouble understanding what there saying? I never have a problem with American words
I could think of three explanations on why you understand American words.
1. Cultural imperialism. Flipping on the telly in the UK you are more likely to find American shows (Friends, Heroes, etc) than flipping on the telly here in the US and finding British shows (usually PBS and BBC America). Likewise, Hollywood is everywhere, but besides Harry Potter, LOTR, and Simon Pegg, there's really not that much coming from UK to the US. So, you have more exposure to American slang than I would have to British slang.
2. You use the context to understand the meaning of the word, but perhaps you really don't. "Rolling in my 6-4" means what? From the context of "Let Me Ride" you probably understand he's talking about cruising. Snoop's specifically referring to his '64 Impala, but you don't actually need to know that "6-4" is a reference to his Impala. For me, I didn't really know what "chavvy" means, I just look at the riced out Escort Clarkson's pointing to and go "ahh..."
3. There is no such thing as "American words." The US is a big place and the "American words" you hear are probably pretty generic. For instance, do you know what chitterlings are? Or how its pronounced in the vernacular? Bubbler? Dubs? Flyover country? Rust belt? Crunk? If someone offered you "fry sauce" would you take it? Do you roll in the 312? Ever been to chi-town? Can you do the Potomac two step?
I think most of these are fairly localized (you rarely hear someone from Kansas City talk about "Flyover Country" and "bubbler" is a fairly Wisconsin/Minnesota phenomena). And fry sauce is unique to Utah. And chi-town refers to Chicago.
Even something as innocuous as "I'm from the 818" is tricky. You'd have to know that 3 digit codes refers to area codes and then know that 818 is an area in Los Angeles.
Just my thoughts about it, feel free to disagree.