This is probably because they are actually measuring hyperactivity when there is universal care versus 40% of it going unmeasured.

Even if you assume the statistics for hyperactivity are correct, how did the researchers decide which statistics were relevant?

In any case, the original 2008 publication is at https://www.nber.org/system/files/working_papers/w11832/w118... . That's long enough ago that we can read how academics interpret the study.

For example, https://www.sciencedirect.com/science/article/pii/S088520062... attributes the problems to the increased used of lower-quality for-profit and unlicensed providers:

"To address the growing demand for ECEC spaces as the cost of care went down, the province saw an expansion of both for-profit and unlicensed home care providers. Data from the aforementioned longitudinal study indicated that 35 % of center-based settings and 29 % of home-based settings were rated as “good” or better quality, compared to only 14 % of for-profit centers and 10 % of unlicensed home care providers. Furthermore, for-profit and unlicensed home care settings were more likely to be rated as “inadequate” than their licensed counterparts (Japel et al., 2005; Japel, 2012; Bigras et al., 2010). At the same time, Quebec experienced a decline across various child health, developmental, and behavioral outcomes, including heightened hyperactivity, inattention, and physical aggression, along with reduced motor and social development (Baker et al., 2008; Kottelenberg & Lehrer, 2013). These findings underscore the challenges of maintaining high standards in the context of expansion associated with rapid reduction in the cost of ECEC."

https://www.tandfonline.com/doi/pdf/10.1080/19345747.2023.21... also affirms the importance of quality

"Meta-analyses have, quite consistently, shown targeted preschool programs—for 3 to 4-year-old children—to be effective in promoting preschool cognitive skills in the short run, with effect sizes averaging around 20–30% of a standard deviation (Camilli et al., 2010; Duncan & Magnuson, 2013). There is also some meta-analytic evidence of persistent effects throughout adolescence and early adulthood on outcomes such as grade retention and special education placement (McCoy et al., 2017). The same is true for universal preschool programs in cases where structural quality is high (i.e., high teacher: child ratios, educational requirements for teachers), with effects evident primarily among children from families with lower income and/or parental education (van Huizen & Plantenga, 2018).

There are, however, notable exceptions. Most prominent are quasi-experimental studies of Quebec’s scale-up of universal ECEC subsidies (Baker et al., 2008; Baker et al., 2019; Kottelenberg & Lehrer, 2017), covering children aged 0–4. These studies found mixed short- and long-term effects on cognitive- and academic outcomes (for example, negative effects of about 20% of a standard deviation of program exposure on a Canadian national test in math and reading for ages 13 and 16, yet with positive effects of about 10–30% for PISA math and reading scores; Baker et al., 2019). Consistent with effects of universal ECEC being conditional on quality ..."

The van Huizen & Plantenga citation at https://www.sciencedirect.com/science/article/abs/pii/S02727... has bullet points "The results show that ECEC quality matters critically.", "The evidence does not indicate that effects are fading out in the long run." and "The gains of ECEC are concentrated within children from lower SES families." In more detail it also cites Baker et al 2008, with:

"In fact, the research estimating the causal effects of universal programs is far from conclusive: some studies find that participation in ECEC improves child development (Drange and Havnes, 2015, Gormley, Gayer, Phillips and Dawson, 2005), while others show that ECEC has no significant impact (Blanden, Del Bono, Hansen and Rabe, 2017, Fitzpatrick, 2008) or may produce adverse effects on children's outcomes (Baker, Gruber and Milligan, 2008, Baker, Gruber and Milligan, 2015). As societal returns depend critically on the effects on children's outcomes (e.g. van Huizen, Dumhs, & Plantenga, 2018), universal child care and preschool expansions may in some cases be considered as a promising but in other cases as a costly and ineffective policy strategy."

I suspect that if the sample pre universal care was big enough, then the measurement of 40% is still good.