Richard, you've pretty well summed up what all of that was leading up to. Does the cable make a difference, and how much difference does it make?

That said, here at my house the cables running right now are quite thin (and very old having been moved several times), they don't have very many strands of wire in them and a few will sometimes break off during attachment, so every so often I'll trim the wire end and start again with the full number of the strands. Since strands are adjacent to each other in the casing the signal would be distributed through the whole cable, even if a portion of them are connected, is my non-electrician's guess.