The Boonville Advertiser mentioned Joseph Rutherford often. Therefore it seems likely they are talking about the same person here.
I can't understand this, "it could just as easily be someone else called John who may be from somewhere else" argument at all. There is a difference between what is possible and what is probable.
I guess it's remotely possible that it is someone else, or that some other kind of mistake is involved (newspapers are known to make mistakes) but that doesn't make it likely. And there's no such thing as 100% certainty anyway.
"Burden of proof" rhetoric is thrown around too easily. Another "canon" of proof is that it's impossible to prove a negative. So in a certain sense, to ask for "proof" this isn't another JF Rutherford is to ask for the impossible. The circumstantial evidence indicates it's probably him. If more evidence can be found well and good, but it's a fair conclusion in the meantime.