The US has said they won't (as a government) lay claim to extraterrestrial material returned to the US from space in this law.
Where the fuck does Russia and China come into this again? They're free to pass their own laws saying that they will confiscate (or not) any material brought back to their territories, and then we'll see just how much shit gets de-orbited into their territory.
I know that if I was running some mining operation, and a particular nation was overtly hostile towards my rights as the person who went out there to get this shit and bring it back, I'd make damn sure that I'm landing it far away from them. The world is a big place, and it would be rather easy to compute a landing trajectory that misses Asia completely. NASA has been doing it for 50+ years.