Always take the opportunity to note that public schools cannot refuse anyone. Private schools can kick out low performers if it could help raise the average student performance on standardized tests.
... which doesn't necessarily mean preferring a better school that's only better due to selection bias (and knock-on effects from being able to remove very-disruptive or low performing students) is a bad way to go, at the individual level, if one has that option. The observation's more relevant to policy-making, than to the relative merits of those options to any given family.
One of the consequences of our state (Washington) going to a state-wide student funding model is that public schools really don't want to lose their non-special education students, because they get a fixed amount of money per student and if they lose too many of the students to private that don't need (and don't get) extra resources, they don't have enough funding to provide programs to the rest.
Yep, absolutely, and that part of their ability to select their students is a major factor in the "look, private schools can educate kids for less than public schools spend, with similar or better outcomes!" sort of stats that get passed around.