The HSA guidelines say that HSA qualified distributions can be made for dependents even though they may not be covered by the HDHP. If a parent is a qualified dependent (i.e. meets IRS guidelines and is taken as a qualified dependent on their tax return), can their expenses also qualified as an eligible HSA distribution?

Yes. An HSA may pay or reimburse qualified medical expenses of a non-HDHP covered dependent (as defined in Code Section 152), to the extent that the amounts are not compensated for by insurance or otherwise [IRC 223(d)(2)(A)]