Is doubting a claim more taxing in terms of energy spent by the brain?
Overall, the claim seems to be that people prefer holding their current beliefs. This is well-documented, for example in a big literature on https://en.wikipedia.org/wiki/Cognitive_dissonance . Note that this may be culturally dependent; some Buddhist traditions explicitly value holding contradictory beliefs.

It's possible the study being referred to in the quoted passage is reported in this paper: https://journals.sagepub.com/doi/10.1111/j.1467-9280.2008.02226.x 'When the Truth Is Not Too Hard to Handle: An Event-Related Potential Study on the Pragmatics of Negation' (One author is at Harvard).

If so, the quoted speaker's comments are inconsistent with the findings. There was earlier work suggesting statements with negations might be more difficult to understand, but this paper doesn't find that. Their results "...suggest that negation poses no principled obstacle for readers to immediately relate incoming words to what they hold to be true."

I think it's fair to say that humans limit the mental effort they put in; this perspective is also summarized in the theory: https://en.wikipedia.org/wiki/Cognitive_miser

A word of caution: the quoted text seems to rely heavily on vague appeals to authority (e.g., Harvard) rather than references to specific empirical findings. This can be a red flag for argument quality.