[it] Having had a quick skim of the rules (Pg 4 Troop Definitions and Pg 36 Close Combat Rear Support) I'd say you are correct from a literal perspective. Troop "type"s are El, Kn, Sp, Ax, WWg et al whereas the grade distinguishes an element's "efficiency relative to the average for that type". Rear support conditional on type *and* grade is explicit elsewhere in the schedule of rear support factors, qv Pikes, Spears, Light Horse, Bows et al. The absence of such explicit wording for Ax(S) tends to support your position.
I'm not certain this was the writer's intention. I suspect this little lacuna arises from inclusion of Wb in the same sentence (where it seems entirely plausible that Wb(O) should be able to support a front rank of Wb(S), eg Saxons, Gauls) and the overarching drive to be ever more conservative with words.
Cheers,
Ivan.