Waterfall is indicative of air in the coolant system; It does not in any way tell you where it is coming from.
The decrease or absence of the waterfall sounds once the car is warm is either due to the coolant expanding to the point that the air can be and is pushed out of the system via the radiator cap or it is being whipped into the coolant and as such simply doesn't exists in large enough pockets for you to hear the coolant trying to push past it.
If you don't trust the radiator cap, get it tested.
If you replace it, test the new one. Toyota only sells two different types of cap for the MKIII, they work a little differently but the both behave the same way. The only other difference is the mount and sealing area.