Maybe I didn't spell it out well enough. So I'll let H. L. Mencken try: "For every complex problem, there is a solution that is simple, neat, and wrong." In this case the assumption that blows up is that the CO2 is evenly distributed throughout the atmosphere. We now know that assumption is wrong in two dimensions. CO2 is heavier than air, so anthropocentric CO2 tends to stay in the lower atmosphere, where it does not contribute to radiative forcing or global warming. (CO2 from volcanoes is injected into the upper atmosphere, and tends to stay there. But that is a different issue.)
The other simplifying assumption that fails is that anthropocentric CO2 is distributed evenly in latitude. NASA has some nice animations which show just how wrong this is--there are two belts of anthropocentric CO2 in the mid-latitudes in both hemispheres, while the CO2 concentration in higher latitudes and at the equator is much lower.
Put it all together, and anthropocentric CO2 doesn't do much forcing, if any. But remember what I said, that I am very much in favor of reducing CO2 emissions because the current levels are already killing people--but elderly people and people with asthma, not by global warming.
A good test of how well someone understands the issues is their attitude towards nuclear power. Nuclear power is the only remotely reasonable replacement for base load coal plants today. You are allowed to be opposed to liquid metal fast breeder reactors (LMFBRs) but that is a detail. I don't know of anyone who still wants to build LMFBRs to close the nuclear fuel cycle. Today, gas cooled and molten salt breeders are a much safer, and actually less expensive alternative.