No this statement is not true
Explanation:
There is no relation between Karma and born in high caste. Karma can e defined as the good deed and actions of a person which decided their future or next birth. We have all heard that your Karma never leave you.
The good deeds or action done by you backs to you in a good thing while your bad works and actions backs to you in bad results. High caste is not related to the good karma.