The fact is: Whitley Rd, Jln Toa Payoh, Jln Kolam Ayer and Paya
Lebar Way are the roads that formed part of the current PIE. Due to
historical reasons their names were kept after its completion. I
would consider them to be part of the PIE. If you refuse to accept
this fact then explain to me why is that stretch of road named Jln
Toa Payoh?
I believe you are hallucinating yourself. Though Pan Island
Expressway =/= Jln Toa Payoh, Jln Toa Payoh = Pan Island Expressway
since its part of it.
56 and 57 do run part of the PIE, though its just for 1 pair of
bus stops.
Precisely the point I was pointing at 
If one were to look at the Singapore Map, PIE "ends" at Eunos
Flyover, which is then preceded by Paya Lebar Way, then Jln Kolam
Ayer where the KPE entrance/exit is, then Jalan Toa Payoh, where
thereafter it is the PIE again.
The names were merely kept for whatever reasons they were, but
they are, nevertheless, they are on the same stretch, running
parallel (be it the slip roads by the side where the bus stops are,
or the middle portion of the stretch where cars are allowed to
travel thru without exiting).