I think a better way to say it is that the brain
doesn't commit to long term memory things that it doesn't need.
I remember hearing about some research they'd done on "binge watching" -- basically, if you have two groups:
1. One group watches the entire series over the course of a week
2. A second group watches a series one episode per week
Then some time later (maybe 6 months), ask them questions about the show, and the people in group 2 will remember significantly more.
Anecdotally, I've found the same thing with Scottish Country Dancing. In SCD, you typically walk through a dance that has 16 or so "figures", then for the next 10 minutes you need to remember the figures over and over again from different perspectives (as 1st couple, 2nd couple, 3rd couple etc). Fairly quickly, my brain realized that it only needed to remember the figures for 10 minutes; and even the next morning if you'd asked me what the figures were for a dance the night before I couldn't have told you.
I can totally believe it's the same thing with writing with an LLM (or having an assistant write a speech / report for you) -- if you're just skimming over things to make sure it looks right, your brain quickly figures out that it doesn't need to retain this information.
Contrast this to riding a bike, where you almost certainly used the skill repeatedly over the course of at least a year.