[Y]ou do authorise the examiner as PIC.
Are you saying that I, as PIC, am authorising the FE to be PIC? There mere articulation of the concept highlights the paradox.
I’ve always treated ICUS as available only to AOC holders in relation to pilots who fly under the authority of the AOC. In those circumstances the AOC holder does have statutory authority to authorise pilots to be PICs of aircraft operating under the AOC. In other words, it’s neither the ‘PIC’ nor the ATO/FE that’s deciding who’s ‘in charge’ - it’s “the operator” (to use the words of the definition of “pilot in command under supervision” in Part 61).
(Why read CAAPs? That way lies madness. A CAAP is just the strong opinion of someone in CASA as to how that person thinks the law should work. The law determines how the law actually works.)