Above ground pool surface question
The concern the manufacturer is apparently trying to address is stability. Given the weight of that quantity of water the posts (or worse yet, some of them) may sink into a soft lawn possibly causing one side of the pool to collapse. This is even more likely if the pool base isn't completely level.
Given the surface conditions you describe I can't see that as a high risk but you have to determine that since you are the one on site. It's another case of the manufacturer playing CYA.
Having said that, it's not a big deal to put a piece of 2x6 under each post just to be certain.   I think more important is getting the area as level as possible before you fill it.