I know Inquisitors have the rule because you don't have to buy them any psychic powers - the rule is there to say that they count as psykers even if they have not been given psychic powers and/or wargear.
An important thing to be aware of is that some models have abilities that behave like psychic powers, but are not. Chaos Daemons are one example, Necrons/C'tan are another. Their abilities look magical but trigger like war gear, and can't be affected by things like Psychic Hoods or Shadow in the Warp, etc.
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