Crothian, sometimes D&D uses "defined" words (like "initiative") to mean very specific things. If you see "initiative" in a D&D book, 99% of the time, it's going to be the D&D defined term. But not every single word in the book is defined. Sometimes they mean things in plain english. A "purely mental action" is not a defined type of action, it's just the plain English sense. An action that is purely mental. If you only allowed actions specifically mentioned to be purely mental, you'd be disallowing all kinds of stuff that doesn't make any sense, including (but not limited to):
Ghostwise Halflings' telepathy
Paladin's Detect Evil
Barbarian's Rage
If you rule that tese actions do require some kind of physicall action (and, in the case of spell-like abilities, like the Detect Evil of the Paladins, you'd think physical actions would give them a somatic component!) you need to figure out what kind of physical action it is, which isn't covered by the game.
Personally, I think it's pretty obvious. If an action requires no physical movement, then it must be purely mental!