False counterexample is a common fallacy/propaganda method, especially regarding group characteristics/differences.
The existence of individuals measuring high and low in all races
Race denialists often use false counterexamples. If race realists argue that a group on average measures high on some variable, then race denialists may cite as a false counterexample the existence of an individual from the group who measures low. Conversely, if race realists argue that a group on average measures low on some variable, then race denialists may cite as a false counterexample the existence of an individual from the group who measures high. However, the existence of such individuals does not prove that the group averages are equal.
This can also be seen as an example of misleading cherry picking by the race denialists.
The race denialists are often attacking a straw man, falsely stating, or implying, that the race realists argue that all group members measure high/low, when the race realists instead make arguments regarding measured group averages.
Fertile river valley civilizations
Race denialists may cite the existence of fertile river valley civilizations as false counterexamples against race realists. See Race and intelligence: Historical societies and in particular the section "Fertile river valley civilizations".
False counterexamples are common in genetics denialism more generally, especially regarding politically sensitive characteristics, by pointing to examples of environmental influences, and falsely stating that these are counterexamples against genetic influences.
The race genetics denialists are often attacking a straw man, falsely stating, or falsely implying, that the genetics realists argue that genetics is the only factor having an influence, when they instead typically argue that both environmental and genetic factors are important.
Counterexamples are common when trying to discredit stereotypes. The validity of this may often depend on what the stereotype claims exactly, such as if the stereotype makes a claim regarding all group members, makes a clam regarding a group average, or makes a claim regarding relative risk compared to other groups.