Personally I find it rude because it subverts the point of being a team in an open office. I think they should speak English at work, just as if I worked in China at a Chinese company I would be expected to speak Chinese. (Unless you're a salesperson on the phone with a foreign company or something)
It is also not "inclusive" for all the diversity and inclusion we hear about, but I would never say this to my manager because I'd probably be called a racist and fired. Plus he's also on a H1B (from India so he speaks English all the time at least).
The Duke email did say that when they are in a professional setting, they should speak English. Med school is somewhat a professional setting, so I see where she's coming from. I don't think she should be fired for that. If they're just in their dorm rooms then I think it's overreaching to ask them to speak English but if they're at a hospital working, it seems useful to ask them to speak English while working.