Not all x-files are setup as tiny is. The recursive function you reference was written for the generic x-file format in which it's valid to have a mesh associated with any frame.

For a statically displayed mesh (no bone animation), the parent structure of the frame to which the mesh belongs is the only relevant data. The transform of the frame it belongs to, combined with the transforms of that frame's parent(s) determine where and with what orientation to display the (static) mesh, usually the bind pose.

For an animated mesh, however, any number of bones can influence it, usually limited by the capability of the graphics card used to display the animation. In the mesh data (in addition to the vertices, normals, tex coords, etc.) are blocks of data called XSkinMeshHeader and SkinWeights. Those blocks of data determine the maximum number of bones and which bones influence that particular mesh, no matter what frame the mesh belongs to or where in the hierarchy the bone resides. In particular, the SkinWeights data determines how much influence (weighting factor) each bone has on which vertices of that mesh. The AnimationSet data, which appears elsewhere in the file, determines how each bone is animated over time, independent of the mesh or meshes the bones influence. As the bone orientations change over time, they "drag" the mesh vertices with them, according to the skinweights. You can look up more info on those blocks.

EDIT: There is nothing that prevents several meshes from being declared in an x-file, each associated with a different frame. However, just as a general observation, most animation x-files have a single mesh, sometimes belonging to a bone frame, sometimes not.