Backing this up with a bit of theory:
Offsetting 4 centre caps by 90 degrees will make you solve 4 edges offset by 90 degrees, in a 4-cycle manner, and a 4 cycle is an odd number of piece swaps, which cannot happen in an odd cube, so 1 more extra swap will show up as the PLL parity.
Void cube parity exists because we may unknowing create a 4-cycle in the E slice, causing the 1 more extra piece swap to happen.