this comes down to defintions, as SO MANY of the sticky topics seem to.
basically there is no magic "tarantula" spiders. there is a group of spiders "scientifically" called myglamorphs that tend to be larger, live longer, and be hairy looking. this includes the australian funnel webs, trapdoors, tarantulas.
some ppl call all myglas tarantulas
there is a specific family in the myglamorphas called Theraphosidae that is traditionally called tarantula in the USA and maybe europe.
as far as i can tell, neither camp is "correct" as it is all a bastardization of a name given to a freakin non-myglamorph spider in the Italy area of the world. i tend to use the theraphosidae = tarantula and call the rest of the myglas "myglas" or something like that
as long as definitions are considered and/or provided things can be relatively simple. i swear half the time there are arguments on here is it because the definitions of the words being use are not agreed on by both sides.