Answer: Yes, it is possible that this student's parents are both the true biological parents.
Their genotype must be heterozygous for the blood type A (AO).
Explanation: Each blood type is controlled by two alleles. A and B are dominant while O is recessive. For two parents that have blood type A to have a child with a blood type O, the both of them are heterozygous for blood type A, this means that each of them has one A dominant allele and one O recessive allele. Their genotype can be represented as AO. The child with blood type O is inherited one O recessive allele from each parent, that is she is homozygous for the blood type O. AO x AO = AA, AO, AO and OO.
AA and AO will manifest as blood type A while OO will manifest as blood type O.
See the attached punnet square for more information.