Avoiding adjustments for time-varying controls in difference-in-differences (DID)?

In difference-in-differences (DID) analysis, it seems like a "folk theorem" that one should be very wary of adjusting for time-varying controls. The reason, eminently plausible, is that time-varying controls may be affected by the treatment, and hence adjusting for these variables will bias the estimate for the treatment effect.

For instance, Alberto Abadie makes this point in the following lecture (around 1 hour into the video; also see Abadie’s slide image below):

https://www.aeaweb.org/webcasts/2014/Econometrics_Jan6_pm/NewStandardPlayer.html?plugin=HTML5&mimetype=video%2Fmp4

QUESTIONS:

1. Does anyone know of citable references (peer-reviewed articles, textbooks) for this rule? I see this rule being used in published empirical work but not discussed.
2. Do people disagree with this rule? If so, why? Any citations which discuss the disagreement?

[Side Note: I understand that James Robin’s Marginal Structural Models (MSMs) explicitly address the issue of controls that may be affected by the lagged treatments. My concern here is the DID method.]