What is different without the parent measures
Four things change when the parent measures come out, and one of them matters for how the companion study reads.
The police result gets stronger. At a fixed count it goes from -0.023 on eight organizations to -0.028 on seven, and from about eight percentage points across the crime scale to about ten. Parents' groups was the other tie that fell as the reported crime level rose, so removing it leaves the police alone as the one organization that does not become more common.
The substitution result does not shift at all. It never used parents' groups. Social services +0.053, mental-health providers +0.051, juvenile justice +0.008, the same to three decimal places.
What the school runs for itself gets much weaker, from +0.48 to +0.232. The formal parent-consultation process was carrying about half of it. The companion study ranks what a school has built above where it is. That ranking holds here, by a smaller margin: +0.225 against +0.094 rather than +0.48 against +0.08.
And the central null weakens. The companion study reports that no measure of the student body predicts how many organizations a school works with. On seven organizations two of the three separate from zero: the share expected to go to college at -0.045 and average daily attendance at +0.034, both small and pointing in opposite directions. Advantage still does not buy reach in any straightforward way, and the claim is no longer as clean.