I'm pretty sure this is not true. They slow down the device when battery can't provide enough current to sustain unthrottled CPU. Its happening in the latest iOS. It happened with my 5 year phone few months ago which suddenly turned off. I don't even feel this throttling but it doesn't turn off anymore.
On an unrelated note, my Google Pixel 7 just hanged up. It didn't happen to me since windows XP I think. It's the worst phone I've ever owned.