Just as a side-note, in EASA-land the rule is not quite the same; AMC 20-6 Appx 4.8 "Diversion Decision Making" has a foot-note;
Note: for an ETOPS en-route alternate aerodrome, a published RFFS category equivalent to ICAO category 4, available at 30 minutes notice, is acceptable.
And that's it. RFFS Category is not mentioned in "APPENDIX 5 - ETOPS EN-ROUTE ALTERNATE AERODROMES", but then who expects logic in EASA documents. Like S 'n R, I suspect that the reason that CAT 4 is OK for an ETOPS diversion is that insisting on the normal CAT for the aircraft (eg 8 or 9) would deny ETOPS operations on many routes.
CAT 4 provides about 20% or less of the capability of CAT 8 or 9 (depending on how you measure it) and would be virtually useless for CAT 8 or 9 aircraft in the circumstances envisaged by regulators who require an RFFS to be present at all, but hey, let's not worry about that when insisting on adequate RFFS facilities would prevent ETOPS operations, which in themselves are little more than a psuedo-scientific statistical comfort blanket that ignores other uncomfortable, perhaps unquantifiable, realities. But that's another subject that we don't need to pull out yet again.