I agree with your reasoning, but DOW and SPX always move more or less in tandem everyday. This has been the case going back as far as I started trading. Check the two charts. Naz, of course, doesn't follow this logic. It moves on it's own terms and conditions.
YM and ES intraday charts have been diverging alot lately. Not sure the reason for that, but one can often give a hint to where the other is going.