Why assume approximates over actual when either could be true ? I agree that they could be approximates but I disagree that that is the only possible assumption. In fact the more thought I give to the separate measurement for a rim the more that seems likely to me.
Although I am comfortable using both literal and metaphoric/allegoric interpretations in this case I don't see the same dilemma you see. And as a scientist I am surprised you could not entertain the two circle theory as being equally valid as the approximate theory.
Occam's razor. The "two circle" idea requires some gymnastics, while attributing the discrepancy to an approximation doesn't.