There are also the small matter that due to glaciation there would have been much less plant life, and animal life to either consume or exhale CO into the atmosphere. In addition those same ice sheets also increase the albedo of the planet, reflecting more sunlight than it would have otherwise, which would also have impact not only on temperature but potentially the interaction of greenhouse effect in the atmosphere.
This is a good part of the criticism of interpreting her correlation. Much of the correlation comes during the retreat of glaciers from the northern hemisphere. But the glaciers have mostly already retreated from the northern hemisphere-- this effect isn't likely to operate.
That said I think it is a no brainer that there is obvious correlation of CO and temperature. Only that it isn't that simple in all but probably the models being built.
The modelers have a damned-if-you-do, damned-if-you-don't dilemma. When the models are simple, people snipe "but the models are too simple; they can't be right." And then when the models are more complicated, people snipe "but the models are too complicated; you can't understand all those feedback loops."
Heck the simple fact that there are Billions more mouth breathers on Earth are likely going to impact the CO levels regardless of industrialization and using sequestered carbon sources (oil, coal, wood, etc...).
Respiration turns out to be a pretty trivial source of carbon dioxide.
(Cutting down forests, though, may be more important effect.)
...The issue is, and always has been a political one and convincing less developed countries to not do what the developed countries did to get ahead, which as you can imagine is pretty hard to do.
If the developed countries find ways to maintain a high standard of living with less carbon usage, I think it's likely that the less developed countries will adopt the same approaches.
...It is all well and good for countries to try and limit their production of CO, but ultimately to do so they tank their own economies (and election hopes), for little good when other countries do not follow suit and are not about to.
It has been a right-wing obsession that reducing carbon dioxide emissions must "tank the economy" but I see no evidence whatsoever that this is the case. We are very very good at resource substitution. Energy is a resource. There is no physical reason we need to burn six tons of carbon per person per year to maintain our standard of living, we just happen to find it convenient to do so.
In the end, it really is a technical problem, and, hard though it is to believe it in this cynical era, we are actually very good at solving technical problems.