When you are measuring voltage drop, dont forget the negative battery cable is just as important as the positive one, and often runs down low in the engine bay, close to water, salt, etc. often the negtive battery cable does not connect directly to the starter, but depends on another length of wire from frame to starter, or frame to bell housing, etc. Some of these connections can be really feeble.
When a franchise shop tells you that you need a starter, I wish I could say that I would believe them. There are honest mechanics and service techs out there, but my wife's sisters have gotten lot of B S from mechanics.