https://www.techrxiv.org/articles/preprint/The_Carbon_Footpr... cites Bender, E.M., et al., 2021, On the Dangers of Stochastic Parrots: Can Language Models Be Too Big?. ACM Conference on Fairness, Accountability, and Transparency.

In short, Jeff Dean (and others at Google) cited the finally published (not by Google) version of the Parrots paper. The citation [20] is in the context of the paper:

"The opening quote in Section 1 is based on a 2019 study from the University of Massachusetts (UMass) that estimated the environmental impact of training [2]. More than 1000 papers cite this paper as the source for the impact on carbon emissions of ML models, e.g., [1,6,7,17,18,19,20]."

in which the authors of this paper point out that the Parrots paper used what is likely a large overestimate of the carbon emissions from training. This is consistent with my understanding (that the power/emissions part of the Parrots paper isn't well backed by evidence).