It definitely differs from UK to US. Here, access is very simple, as long as you are prepared to pay.
When travelling to the US, it happens that most of the courses one would want to see and play are private, so you need connections. A large number of people are fortunate to have fellow members at their clubs with connections at various places, or who know people that do. Your pro will often help out.
I have hosted many people, and indeed friends of people. I've never had a bad experience. I would hope that I have been a decent guest when visiting the other side of the Pond!
What I would also say is that in my experience members of world class clubs in the US tend to be some of the most helpful, gracious and accommodating people, and go out of their way to help when they know you.