I agree that these two group monikers are accurate because they both define generations of a 20 year period of when the contestants where born. The show is trying to show us the difference between two age groups in reality survival experience and naming both groups by their respective generation bracket is an accurate statement.
Yes, the two group monikers for Millennials and GenXers are correct, because there are a lot of distinctions between the two generations. GenXers came of age in a time of peace. They protested for fun. Millennials came of age during a recession. They know what hardship is. These differences create a large culture gap between the two generations.
The names and distinctions are kind of stupid. People are not devided so easily into these catagories, and the terms have been used as insults. Millennials has been used to call people lazy or conceited or self centered, but there is no series of descriptions that describe any large group of people.
The term "millenial" does not accurately describe the entire generation that it is meant to encompass. For people born in 181-1988, they did not grow up with cell phones or computers and are vastly different than the 20-somethings of today. The term Gen X, however, leaves them out too. The people born in these years did not grow up in the revolutionary 60s or 70s either. Under these "generational" terms, those born in the 80s are left out.