"What is there to reconcile? You know what a "back-formation" means, right? First there was a noun "homeopathy," and then ... "homeopath." It just comes from shortening the form of the word, it no longer relates to the original root histories."
You're absolutely right, there is not need of reconciliation, or even slightest agreement with etymology in cases of back formation.
back-formation
n : a word invented (usually unwittingly by subtracting an affix) on the assumption that a familiar word derives from it.
"There are lots of back formations but naturally all examples escape me."
The typical example is "Utopia" (Gr for nowhere land). But one of the most illistrative examples is "cheesburger".