Honestly I kinda hate that saying. It's like "it's not the fall that kills you, it's the sudden decelleration on impact." For most situations people encounter, it's high voltage sources with more than enough power which are dangerous.
Even 50mA will likely kill you, as outlined on the "death graph" as we electricians call it. This is independent of voltage.
https://upload.wikimedia.org/wikipedia/commons/7/7f/IEC_TS_6...
Blue is harmless and imperceptible, green is harmless, yellow is harmful, red is fibrillation.
Edit: This illustrates why 30mA (or less) RCD protection is common (and required) in various jurisdictions, depending on the kind of circuits you're serving.
But at higher frequencies, you should experience the skin effect, right?
That said, we're referring to power delivery here, and the highest frequency I'm aware of in this space is the 400 Hz power distribution systems used on warships.