Does the transform.parent hierarchy have any relationship to the bone hierarchy?
Well it is the bone hierarchy. The relationship between the bones and the mesh vertices appears to be a separate thing to do with the ordering of the SkinnedMeshRenderer bones collection.
If you move a parent transform then all the subsequent child transforms are moved. So rotating the upper arm rotates the elbow and all bones below it.
Mixamo rigs are well labelled and clear to understand, worth looking at one of their characters. Pretty sure that there’s a free zombie on the Asset Store.
(or am I still missing the point about what you are after 