The claim for child support is actually the child's, not the mother's. Based upon this, I don't see how ANY sperm donor can (logically, anyway) avoid liability for child support, absent specific legislation. The unborn child cannot give its consent to waive child support from its "daddy." The only real shield is anonymity, and that would seem to be penetrable (so to speak) by a sperm bank's records. Just my $0.02 worth.
I think you are correct.
A bank which violated a contract by releasing identifying information would be liable to the donor for any resulting support awards.
As for the "child's right" argument, I don't buy it. Legally speaking, this is exactly the same theory by which unethical lawyers like John Edwards have put thousands of obstetricians out of practice. No matter how many liability waivers the woman signs before the obstetrician assists in the delivery, these creepy lawyers get them all thrown out on the grounds that the mother didn't have the capacity to waive the child's right to sue the obstetrician. This same theory results has led to the insanity of many schools enforcing "no running" policies on their playgrounds -- if a child sustains a serious head injury after running headlong into a wall, ambulance-chasing lawyers will successfully sue the school (or district, if it's public) for millions, saying that the liability waivers the parents signed when the child was enrolled aren't valid, because they didn't have the right to waive the child's rights.
Children don't come into the world with a "right" to money. Their biological father is free to shoot himself the day the child is born (and for that matter, so is the mother), and plenty of children in the third world are born to parents who don't a dime between them. In a case like this, where it was clearly the mother's decision to bring these children into the world (she accomplished it via an IVF clinic, and paid for it herself), a written contract absolving the donor of support obligations should be enforced. But alas, these two dim bulbs didn't bother with a contract. Hope the court leaves him with enough cash to get himself fixed :-)