The above circuit is correct when all the resistances are nominally at the same value i.e. the same magnitude balance current flows into both R1 and R2.
Redraw: I've added a label in red (inside a red circle) called "C". This is the "new lower power feed point" and you can now ignore the old node in black called "C": -
Can you see that R3 is in series with RW2 and equally, R4 is in series with RW1 and hence the balance is maintained.
RW3 is a red-herring because it doesn't imbalance anything when its value changes; it just affects the "gain" of the circuit.