Whether or not your model has animation data is irrelevant. LoadAnimMesh keeps separate objects within a model separate, while LoadMesh merges everything into a single object/entity.
That said, the issue may be that you need to apply textures to separate surfaces, not to separate objects. It's really hard to tell. Use CountSurfaces on your model to see if there are multiple surfaces; if so, texture surfaces individually.
That said, the issue may be that you need to apply textures to separate surfaces, not to separate objects. It's really hard to tell. Use CountSurfaces on your model to see if there are multiple surfaces; if so, texture surfaces individually.