Thanks. I re-read the publication that ColeenD3 linked. I think I understand it now. When it says that a child's social security benefits are considered support paid by the child, it is attempting to make a distinction between social security benefits and state/local benefits (such as TANF and SNAP). The former is treated as support paid by the beneficiary.
I wonder if the fact that I'm my daughter's Representative Payee for her SSI makes any difference. Social Security appoints Representative Payees to receive and manage the funds for beneficiaries who are unable to do so themselves. I suppose it wouldn't make any difference since my daughter is still the beneficiary of the SSI, even though I'm the one who is actually receiving the payments on her behalf.