AFR, BFR, whatever - it's a check done every two years unless exempt in the way you describe, i.e. in a regular check program with a contracting state airline.
But I suspect from reading all the bumpfh on the subject that some form of recognised certification would have to be in CASA's hands before you rocked up on leave and blasted off in a VH aircraft on a private mission. They state quite clearly that they retain ultimate control of such matters (as, being an ICAO contracting state, they must). Hence the additional requirements for an oral back home in Oz to renew an instrument rating.
So how would CASA monitor your AFR status if they don't regularly receive and retain your paperwork?
I shudder to think what the insurers and CASA would have said had I returned from overseas and simply renewed my Australian medical then gone flying privately on an assumption that because my last gig had been with a recognised contracting state, all was kosher. Then ended up inverted in a paddock somewhere.