The Gemara implies that the bones of an animal (when there is no meat on them) cannot become Tamei? Is this true?
There are many different types of Tum'ah. The type of Tum'ah under discussion in the Gemara to which you are referring is Tum'as Ochlin (Rashi DH Mahu she'Yitamei). Only items which are edible can become Tamei through Tum'as Ochlin. Bones, therefore, do not become Tamei.
However, bone can certainly become Tamei in other ways, such as Tum'as Keilim. That is, if a receptacle is made out of bone, it becomes Tamei when touched to a Mes (Mishnah Kelim 2:1).