*sigh* We can all argue this here on a specialized online forum (that has nothing to do with sport, except for the fact that it is occasionally discussed in one of many of the sub-forums), but it doesn't make a bit of difference because
the actual athletes are not concerned at all about international training.
I attended the University of Calgary for 4 years - the Calgary Olympic Oval from the 1988 Olympics is located on the campus and is still considered one of the top indoor training facilities in the world. While at the U of C, I lived and breathed the Oval; I did all of my studying, reading for classes, ate my lunch there. If an international competition was on, I would often skip my classes and spend the entire day there. I had "Oval friends" (who I never saw anywhere outside the Oval) who did the same. And I also had the privilege, as a student of the university, to use the long track ice for public skating from 12:00-1:00; I did so every day that the ice was open to the public during my 4 years at the university. The best days were the days that there were only a few public skaters and they kept the outside lane open to the competitive skaters. Being on the ice with some of the best long-track speed skaters in the world is a thrill that I really can't describe. The highlight of my 4 years at the U of C was the day that Catriona le May Doan ran into my feet as I was sitting on a bench taking my skates off; she gave me a dismissive "sorry" without looking back. It was awesome.
Anyway, my point is that I knew the Oval and I felt like I got a good and accurate picture of the athletes that skated there. Most were Canadian, but there were also many US, Dutch, French, British, Chinese, and Korean athletes who were there on a daily basis; some took classes at the university, others were there strictly to train. They all shared coaches, hung out together and chatted while they weren't on the ice (and were waiting for us schlubs to get our sorry butts off the ice right at 1:00), and discussed their gear and training. You would often see two (or more) skaters from different countries on the ice helping each other out with a technique. This is why people from all over the world travel to their sport "hot spots" - the best facilities, the best coaches, and the feeling that comes from training with the best in your sport. The skaters all knew they would be competing with each other in the next international competition (but then again, you're also competing against your own countrymen) and there were no hard feelings. The international atmosphere was one of the reasons that I loved the Oval so much.
Athletes compete for their home countries, but I don't think there should be any bitterness from us about where they train. There are only so many world-class training facilities in the world.... ideally, you'd want to train in one close to home, but that's not always possible.