Not true. As the author admits earlier, there is a nonzero warming effect from CO2. While the author points out that CO2 generally rose after warming in the geological record, those increases in CO2 also produced increases in temperature up to the point where the positive feedback loop ended. The feedback loop is not infinite because CO2 warming generally decreases as CO2 concentrations increase, other feedbacks are variable (e.g. water vapor) and the forcing eventually changes (i.e. the changes in the sun that the author correctly points to).
This writeup is not particularly scientific, although it does contain lots of true scientific statements and is almost 100% true regarding climate politics.
So the question then becomes how much impact does man-caused increases in CO2 increase temperatures? And is it significant compared to other natural fluctuations in global climate. If it is relatively or statistically insignificant, then we can ignore it, especially if at some point the feedback loop is broken naturally.