The speaker was probably misunderstanding a couple of different facts about our ancestry.
In a nutshell ancestors are much rarer than descendants. All humans alive today can trace their mitochondrial DNA (passed on only by females) to a last common ancestor sometimes called 'mitochondrial Eve' who lived in Africa about 100,000 - 150,000 years ago. Please bear in mind that she was only one of a population of many thousands who no longer have living descendants.
Similarly all men have a Y-chromosome that can be traced back to a single individual - also one member of a large population - who lived at approximately 180,000 years ago. Having said that different studies have come up with different results for those dates but none of them are less than 100K. These are examples of genetic bottle-necks but it is highly unlikely that they occurred within mellennia of each other or in the same population.