There's plenty of law that applies here. There was certainly a contract, and the clinic clearly didn't uphold it's part of the contract (which apparently didn't give the clinic the right to avoid any responsibility for this sort of error as long as they offered the woman in question a morning-after pill in time to prevent the pregnancy). This clinic will end up paying through the nose, and any individuals found to have played a part in withholding the truth from the man will have a heck of a tough time hanging on to their medical/nursing licenses or getting malpractice insurance in the future. However, none of that avoids complications in the child's life, or in the life of the man who (apparently) became the biological father of a child without his consent, due to the unauthorized actions of the clinic staff.
Here is where I think the laws should fix things. Once you hand over your DNA, you no longer have any rights in the ordinary biological sense. Sperm and/or egg donors should NEVER be hounded for child-support or any such nonsense. This is a similar (albiet different) situation. You put your semen in a cup to be used (in certain contractual ways) in a fertility clinic, you should have ZERO biological rights or responsibilities. ALL rights and responsibilities should be contractually defined. The father should NOT be the person whose DNA matches, but should be the person stated in the contracts to be the father. Ditto for the mom.
I don't think the bio-parents deserve ANY legal standing based on biology. The contract, and NOTHING ELSE, should be legally binding.