The opposite. They're closely related
compared to the rest of the world, but still come from different families, while living in substantially similar environments, which in many way have "maxed out" advantageous factors (health, stability, stimulation, etc.).
Remember that the heritable component of intelligence is polygenetic; it'd not determined by the presence of a single SNP, and two people could have similar intelligence originated in very different genetic profiles. People who are relatively closely related will have similar profiles that interact with the similar or shared environments in similar ways, meaning that the effect of small genetic differences will be more pronounced. Someone with the same "potential" for IQ, but from a different set of intelligence-related genes, interacting with the same environment might be said to have had the heritable component of their IQ become less efficacious.
For example, nutrition is a component in IQ. Everyone at this school is able to drink milk and benefit from the nutrition value-add. Someone less related to the other students also attends the school; they're lactose-intolerant, but benefit from eating certain fruits native to their homeland. The school doesn't serve such fruits, but it does serve milk. The student subsequently tests at a lower IQ. I would say at this point that variation between the LP students' intelligence is likely to be more related to genetics than is the variation between their IQ and this lone student's, which has a more substantial environmental component.