Bit more info:
The rainbow was photographed from about 1.8m 1/4000 sec. f11 70mm ISO 800 three speedlites HSS
The juvenile blue faced honey eater about 3m 1/1000 sec. f6.3 388mm ISO 1600 natural light
If the explanation you give assumes stationary subjects [ I'm guessing it does ] then the possibility is that the moiré problem with the image of the rainbow is related to movement of the subject. That would leave me with two possible solutions [ maybe ]:
1. I raise the shutter speed to 1/8000 sec
2. I set up more speedlites at reduced power and hope the duration of the 'flash' [ I am aware of the mysteries of high speed sync ] is small enough to 'freeze movement' [ no HSS just ttl ]
One further possibility would be to set up lights to illuminate the scene continuously, but still apply 1. and 2. above.
What are your thoughts?
All the best Bob