What is the brown sauce in authentic Chinese fried rice?
If it really is authentic, then it is soy sauce. Some recipes also use oyster sauce but I would not call that authentic or traditional.

Soy sauce can mean many things; it might just be a different soy sauce from what you're used to. There are light vs. dark soy sauces, and also fermented vs. hydrolyzed kinds. A naturally fermented light soy sauce would probably be (a) mild and (b) slightly brown.

Some other common types of sauce that I've seen used in stir fries are hoisin and satay. But, as with oyster sauce, I wouldn't call those authentic or traditional. That "some sort of brown sauce" is almost certainly soy sauce. It might include XO sauce, although you would notice a seafoody taste in that case.