In addition, the global history classes that I have taken tend to look at the past 300 years of history as, "Europe and the United States are proactive, the rest of the world is reactive." How is global history approached in other countries, especially non-Western ones?

That's exactly what global history isn't supposed to be. That's what it is supposed to remedy. While historiography as most of us know it has mostly been formed and practiced in Western nations, the global history trend is an attempt to be more all-inclusive and comparative in order to shift the focus away from the Western world and on to a more global scale. So it baffles me that the global history classes you took were seemingly the opposite.

As for your main question, you need to realize that most historians here will probably have done research on topics that are close to home and heart. This isn't necessarily an intentional bias, but an organic one. There aren't just language boundaries to be taken into account, but also the availablity of sources. It's also very human to show an interest in your heritage and the history of your own culture. So while it's not entirely unheard of that a historian ends up specialized in something that is far removed from his country of origin, it's not exactly common.

I'll take my country as an example. I'm Belgian. I can safely say that nearly all of the research I've read on Belgian history - especially at the ground level - has been done by Belgians. It has obviously been read by historians all across the globe, but the initial research is still mostly done by those who were born in Belgium or at least have lived there for an extensive amount of time. They know the the culture, the country and they can actually read the sources.

This is part of the reason as to why Europe and the United States have been so heavily focused upon in historiography. These were historians studying their own culture and when they studied other parts of the world, they were mostly studying them in relation to their own culture. This has started to change the past few decades though and we're seeing very vibrant historical research surfacing all across the world done by local historians. It's a real treat.

I'm sure that the American culture is a lot more appealing to most than the Belgian one, so you might actually find a reputable historian who isn't American and who has studied the United States extensively. It's just not as common as you might think. I for one am fairly certain that I've never read an article on Belgian history that was written by someone who wasn't Belgian or at least wasn't based upon research done by Belgian historians.