Care to post the citation for this claim?
I've read plenty of papers on this but the ability to track "imported CO2" is fairly limited.
The most obvious place that's usually missing in capital gained from foreign investments. If, in a hypothetical example, an investment firm make a billion dollars running a foreign oil company, then put that money into a US startup, this wouldn't count as "imported emissions", but clearly if you worked at that startup your job and all the money you spend would have come from exported emissions.
The second place these studies tend to fail is how long of a trail of CO2 they follow. If one of the reasons it's cheaper to build a product in China is because the factory is closer to a carbon intensive raw material producer this not counted. If the energy to keep your low cost workers is cheaper and that's part of why they are low cost, that's not counted.
It's not the fault of these reports that they can't track all of this, but it's not a great argument for green technology reducing emissions.
If also doesn't matter if the US and EU reduce emissions, it matters if we do globaly. I can also promise you that if we forced China to reduce emissions we should feel that impact pretty dramatically in the west Economically. The best proxy globally to economic development is energy production, we live in a global economy, we all share that energy.