I do see your point and it's a valid one, but you have to remember that we are from the USA and it's promoted here so of course it seems biased....it's supposed to. The Presidents Cup was set up b/c The Ryder Cup doesn't include any countries outside Europe or the UK. In Fact, it wasn't until the 70s(not quite sure when) that the RC allowed European players. Before that is was only players from the UK. We(USA) were always winning so Jack Nicklaus suggested that Europe be added to the UK team to make it more competitive. Eventually there were so many good International players on tour in the US and around the world, that someone, somewhere, decided that an event to include the International players was a good idea.....thus the Presidents Cup.
As far as feeling connected to the International Team goes...well, I'm from the USA so I'm not all that concerned about that. But since Europe is part of the Ryder Cup Team, often times there aren't members from a particular European country on the team. For instance, in the last RC, there were no Germans or French players on the team....in fact, I'm not sure if there were any Swiss players either and I think there was only one Scandinavian player on that team. So as you can see, it goes both ways.
I hope I was able to help you out there.