Two brand-new, publicly accessible review articles confirm that this study had a sampling bias. It's basically children from low-risk, middle-class white backgrounds that exhibit higher cortisol levels in day care. Children from other backgrounds may have positive results, depending on the quality of care.
Child Care and Cortisol Across Infancy and Toddlerhood: Poverty, Peers, and Developmental Timing (2016)
For children from high-risk contexts, within-child increases in child
care hours were predictive of cortisol decreases. The inverse was
evident for children from low-risk contexts. This relation grew across
toddlerhood. Whereas a history of greater center-based child care was
predictive of heightened cortisol levels for low-risk families, this
was not the case for children from high-risk families. Irrespective of
risk, greater peer exposure (between children) was associated with
lower cortisol levels.
A review of research on the effects of Early Childhood Education and Care (ECEC) upon child development (2015)
A recent review of the largest and most representative childcare
studies in the US and many smaller studies concluded that the effects
of quantity of care on children’s behaviour problems were population
specific: for disadvantaged children and those from minority ethnic
families, extensive childcare was not associated with more
externalizing problems – in some cases it predicted lower levels,
possibly compensating for other disadvantages (Huston et al., 2015).