If you don't connect to the ground rod at the pool, you are STILL connected to the ground rod at the house, so is all yourt BONDED equipment since anything electrical like the motor casing/housing will be grounded allready, you're essentially grounding your bonding, EXCEPT you're doing it through a tiny wire that may not withstand a lightning strike (and that's the route a lightning strike would take).
In my opinion, you're safer with a ground rod or six or ten, like I stated before, anything electrical that goes wrong, your pool is tied to your pump, to your GFCI, to your Electrical Ground (which is also teh house ground for anything metal), so anything goes wron electrically speaking, you're safe, the GFCI will pop.
A scenario of why you'd need this is that if your DH would be mowing the lawn while you're in the pool and he accidentally mows over the pump cord, the cut/live end hits the pool, voila GFCI goes "pop" and you live. Electricity would trip the GFCI since it's wired to do so (whether or not you have a ground stake).

A scenario where the ground rods save you is when all electrical is OK, you're swimming (again! Is that ALL you do???), a rogue lightning stike hits the pool, the ground rods take care of it and you live (again! - what do you have, 9 lives or something??)
Oh, BTW - In this scenario, the GFCI may be fried, but hey, you got to live, so that's not a bad tradeoff.....then again, you may want to verify that statement with DH.

Since your pool is sitting on the ground, the second the ground is wet, you essentially have a ground rod anyways since water conducts electricity.
The reason they have you install RODS is so that there is always good continuity to ground - meaning, the rod penetrates the ground so far that the earth it's in is always wet or damp at minimum meaning it will ALWAYS conduct electricity.

So the question to you is - do you feel lucky?