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youre right and its true about the tool and melder effecting each other. it does not make sense, the tools are completely separate from one another. Though, what does make sense is the clothes or equipment currently equipped, as they're suppose to raise your stats in its entirety, melder or no melder. So, as OP said, naked melding having the same effect and chance as materia'd equipment is invalid and makes no sense.
unless the melder has a unique stat (ill have to make one up for hypothetical purposes)(concentration) no matter what gear you add it would not affect the concentration stat since it is unattainable.