That rule—26 C.F.R. § 1.414(c)-5—refers to an 80% overlap in the governing bodies of exempt organizations, which the rule describes as “an organization that is exempt from tax under [Internal Revenue Code] section 501(a)[.]” https://www.ecfr.gov/current/title-26/section-1.414(c)-5.
Although a public-school district is not subject to Federal income tax, that results from law other than I.R.C. § 501(a).
Further, even if one were to interpret I.R.C. § 414 to treat a public-school district and a foundation as one employer, that might not necessarily answer questions about whether a governmental plan may cover the foundation’s employees without losing ERISA’s governmental-plan exemption.