Ummm....what is all the arguing about?
The only time a resistor cannot be in series or parallel is if you isolate it. That means it is hooked to nothing. What is so hard to understand about this? If if the circuit had only one reisistor, you still have impredance you have to take into account with rescpect to the other parts of the circuit. If the resistor is shorting the supply to itself, then it is in series with the supply.
The whole point of delta and wye is that you cannot simplify the circuit into one resistor since they either share a common potential (or node) or the common ground is not common at all. yes, you could say they are not in series or parallel, but to do the conversion, you need to make assumptions on whether they are in series or parallel.