I doubt that was ever actually true. It was probably a kind of shorthand to explain to users that some processors had the right kind of power management to enable efficient always-on speech recognition.

And, another thing, local speech processing doesn't mean you are safe from recording or from large-vocabulary transcription. Compared to what 1980s speech processing runs on, even when throttled-down to conserve batteries, you've got ample processing power in modern smartphones.