To be clear, we're talking about running a country in your home country, not in America, while you are currently on an H1B in America. I'm sure you know more about this than I do -- could you provide me with a link? I'd love to learn more.
It's perfectly fine to own a foreign business (i.e., not located in the US). But it's generally a violation of the H1B to run (i.e., operate/manage/supervise) that business from the US because the foreign business is then generally treated as having a US presence. See "permanent establishment" and the US tax treaty with whatever country you're from.
