Yep, you and they are right. You have twin cooled...because the liquid only cools the heads so it also needs the air cooling.
The additional liquid helps keep the combustion temps from getting out of control (high) so easily but does nothing for the cylinders, which experience friction from the rings as well as heat transfer from the heads.

Technically my 17 RG M8 is also “twin cooled” with oil and air. Yours is “twin cooled” with coolant (water) and air.
“Twin Cooled” is their trademark for the M8 engines that run coolant through their heads.
Bob