I would ground the pool to the rods, reason being, if lightning ever does strike and you do NOT have rods, under certain scenarios, it is not grounded well enough just by sitting on the "ground" (meaning dirt). if the "ground" is not wet enough, lightning will not travel into it, it's the moisture content in the "ground" that allows it to act as a grounding point, the dirt itself does pretty much nothing, the rods ensure that you are always grounding through soil that has moisture content, so essentially they are just an extension of all your pool metal into permanently wet/damp "ground".
Without the rods, If lightning strikes during a dry spell, the path of least resistance would be through the circuit ground wire (the thin one) back to the panel and into the grounding rod located at the house, however, this path would only be available to the lightning for a mili second because that's all it would take to burn up the wire, at that point you would no longer have a path to ground - therefore, to be absolutely safe, I would use the ground rods.

Grounding your pool through ground rods has absolutely NO effect on the bonding aspect of the pool, bonding is a completely different procedure meant for a completely different scenario, but still brings everything back to a ground rod at your house.
Bonding anything metal is done to ensure that if this metal becomes energized, it is safely taken to ground, eliminating any electrical potential within that item. However, bonding is not done for lightning strikes, it is done for electrical malfuntions where the current is much lower and will not cook your #12 wires. Metal things INSIDE your house will likely NEVER get struck by lightning, metal things outside of your house are always at risk, I looked at my Natural Gas tank located outside my house last night, I found a #8 wire leading directly to ground from the tank's body. I looked at my Electrical meter outside my house, another #8 directly to the house ground rod. When I installed my Satellite dish, it was not just recommended, it was specified to ground it within a certain number of feet otherwise the warranty would be null and void.
My pool instructions specified it as well, yes, it's not electrical code, but the pool manufacturer has nothing monetary to gain from this recommendation, yet they still recommend you do it.

BTW - Anything bonded within your house like plumbing, gas lines etc., goes DIRECTLY to the house ground rod through a minimum #8 wire, why would it be such a bad thing to do the same at the pool instead of relying on a thin #12 wire to bring it all the way back to the house just to let the #8 located there bring it to the ground rod?
The code specifies that a ground rod is NOT required, however, that does not mean you cannot install one, codes are MINIMUM giudelines you have to follow, however, like anything, going above and beyond the call of duty is not a bad thing.
I live in Canada, our electrical codes are different, usually our construction codes are stricter that those in the USA, I have not had time to look up our electrical codes on this issue, but this is going to make me do so as soon as i can, I WILL post back with my findings on that.