Dan Rather has quite a lot to do with YF's argument, yes. It is pretty obviously used as a counterpoint to your example about Woodward being credible due to past reporting. In this context, it is quite relevant, although, not incredibly persuasive.
As far as I can tell, YF hasn't mentioned a single time that the Woodward book is BS because of anything about Trump. That is why your post is clearly off-base. What he has said is that multiple people refute statements that Woodward has attributed to them, and the one he sourced was James Mattis.
I'm not saying you have to take Mattis' word over Woodward's, but I am saying that that is the choice his argument gave you. Mattis vs. Woodward, *not* Trump vs. Woodward.