Could an individual with blood type O (genotype ii) be a legitimate child of parents in which one parent had blood type A and the other parent had blood type B?

Yes, This can happen if both the parents are heterozygous.

Explanation:

To have a child with blood type O, both the parents should have at least one copy of allele "i". This is required since the genotype of a person with blood type O is "ii". Parents with blood type A and type B can have a child having blood type O. Here,  the genotype of the parent with blood type A should by  IAi which means that it is heterozygous in nature. Likewise, the parent with blood type B should have genotype IBi.

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