The narrative existed because there was a span of several years where successive updates did make iPhones a bit slower, by virtue of adding more features and complexity. Since Apple makes money by selling you a new phone, some people assumed that it was a way to gaslight you into upgrading. When these people learned of a circumstance where it was definitively shown that Apple did slow down older devices, they took it as proof that their gaslighting theory was true.
My iPhone 4 became unusably slow after an update I could not revert. I liked that device and would have preferred to have it still work if needed in a pinch.
edit: To be clear I would have preferred them not force the upgrade on me. I still would have likely purchased a new phone, but instead I purchased an android phone.