See the full text of the statement that you quoted from IRS Pub 502:

Child of divorced or separated parents. For purposes of the medical and dental expenses deduction, a child of divorced or separated parents can be treated as a dependent of both parents. Each parent can include the medical expenses he or she pays for the child, even if the other parent claims the child's dependency exemption, if:

1. The child is in the custody of one or both parents for more than half the year,
2. The child receives over half of his or her support during the year from his or her parents, and
3. The child's parents:
    a. Are divorced or legally separated under a decree of divorce or separate maintenance,
    b. Are separated under a written separation agreement, or
    c. Live apart at all times during the last 6 months of the year.

This doesn't apply if the child's exemption is being claimed under a multiple support agreement (discussed
later).

With respect to the one claiming your stepdaughter as a dependent, her dad is the "other" parent, not you.  This appears to mean that a distribution from her dad's HSA, not a distribution from your HSA, could be used to pay for her medical expenses.

However, this isn't completely settled.  The question is whether being eligible to be treated as her dad's dependent also means that she can be treated as your dependent for this purpose when you file a joint tax return.  I think the answer is No.  Your stepdaughter's medical expenses could be included on Schedule A as a dependent of her dad, but I don't think that this makes her your dependent for tax purposes.