So says the Bush administration's Office of Legal Counsel in an opinion letter interpreting the effect of the Defense of Marriage Act on the benefits eligibility of the child of a non-biological "second parent" in a civil union:
Although DOMA limits the definition of “marriage” and “spouse” for purposes of federal law, the Social Security Act does not condition eligibility for CIB [child's insurance benefits] on the existence of a marriage or on the federal rights of a spouse in the circumstances of this case; rather, eligibility turns upon the State’s recognition of a parent-child relationship, and specifically, the right to inherit as a child under state law. A child’s inheritance rights under state law may be independent of the existence of a marriage or spousal relationship, and that is indeed the case in Vermont. Accordingly, we conclude that nothing in DOMA would prevent the non-biological child of a partner in a Vermont civil union from receiving CIB under the Social Security Act.
There's a good summary of the opinion letter, the factual background, and the reactions of both supporters and opponents of same-sex marriage and civil unions at Law.com. Peter Sprigg of the Family Research Council, for example, is quoted as being "disappointed" that the administration did not take a "pro-family" position by denying benefits to the child.
I'm no expert on Social Security benefits, but the result seems right as a textual matter under both DOMA, which forbids federal recognition of same-sex marriages, and the Social Security Act, which defines an eligible child as one who has the state-law right to inherit from a parent regardless of the marital status of the parent. A contrary result would have put the federal government in the position of saying that not only is the parents' civil union created by state law unrecognized, but that the legal parent-child relationship created by state law is unrecognized. While it appears the legal parent-child relationship in the case arose from the parents' civil union, rather than from an adoption, the continued recognition of that parent-child relationship under Vermont law, including the inheritance right, is not dependent on the continued existence of the civil union.