However, they do it in a way that makes me think, they don't have any clear evidence, because just saying so doesn't make it so:
On historical timescales, CO2 has definitely led, not lagged, temperature. But in any case, it doesn't really matter for the problem at hand (global warming). We know why CO2 is increasing now, and the direct radiative effects of CO2 on climate have been known for more than 100 years. In the absence of human intervention CO2 does rise and fall over time, due to exchanges of carbon among the biosphere, atmosphere, and ocean and, on the very longest timescales, the lithosphere (i.e. rocks, oil reservoirs, coal, carbonate rocks). The rates of those exchanges are now being completely overwhelmed by the rate at which we are extracting carbon from the latter set of reservoirs and converting it to atmospheric CO2. No discovery made with ice cores is going to change those basic facts.It's true that today the rate of increase is higher, but are the overall levels truly higher? And most of all, what stopped global warming back then? but let's continue first.
What is being talked about here is influence of the seasonal radiative forcing change from the earth's wobble around the sun (the well established Milankovitch theory of ice ages), combined with the positive feedback of ice sheet albedo (less ice = less reflection of sunlight = warmer temperatures) and greenhouse gas concentrations (higher temperatures lead to more CO2 leads to warmer temperatures). Thus, both CO2 and ice volume should lag temperature somewhat, depending on the characteristic response times of these different components of the climate system. Ice volume should lag temperature by about 10,000 years, due to the relatively long time period required to grow or shrink ice sheets. CO2 might well be expected to lag temperature by about 1000 years, which is the timescale we expect from changes in ocean circulation and the strength of the "carbon pump" (i.e. marine biological photosynthesis) that transfers carbon from the atmosphere to the deep ocean.However, they even show that CO2 and ICE-sheet albedo are lagging behind and he even establishes that in those times, the critics were right. It wasn't CO2 that drove climate, but rather the sun and the earth's own imperfect course through space. But the crucial point is the following:
In other words they have given up searching for a better explanation in favor of the just fitting of CO2 increases and decreases (albeit lacking a few thousand years). But if it is true that CO2 is lagging behind temperature, than it can't be the root cause of global climate change, but is rather an ampifying fraction of the whole change.
While we don't know precisely why the CO2 changes occur on long timescales, (the mechanisms are well understood; the details are not), we do know that explaining the magnitude of global temperature change requires including CO2. This is a critical point. We cannot explain the temperature observations without CO2. But CO2 does not explain all of the change, and the relationship between temperature and CO2 is therefore by no means linear. That is, a given amount of CO2 increase as measured in the ice cores need not necessarily correspond with a certain amount of temperature increase.
If we consult some basic science knowledge, we know that the albedo (reflectivity) of the earth is another important factor, also a negative feedback would be water-vapour (due to higher temperatures) which would increase because 70% of the Earth are covered with water. This would significantly increase cloud cover and thus cooling the earth by shielding it from sun-light.
However, somehow scientists don't believe in clouds, because they cannot accurately measure them. Or they underestimate those effects that are not perfectly known.