There are two big issues:
* It is very hard to gut-feel wealth distribution (eg, http://marketrealist.com/2013/10/shutdown-101-perceived-weal...). Identifying who the US rich requires more study of statistics than most people have time for - so this assertion is about a group that is difficult to identify. If most of the US rich were in fact living quietly on family wealth from a generation ago, how would this be identified? How do we verify that these 'rich people' are indeed meritorious? They might not be.
* All of history is a very long time. Although the US is technologically the most advanced nation we have ever seen, to claim that it rewards the meritous more than any nation in history is probably wrong, and suggests grandparent isn't making a point based on careful thought. We have had democracy for more than 2,000 years, the US has only been around for ~300.
[1] https://www.nytimes.com/books/first/s/stanley-millionaire.ht...
Most of the studies I've seen reach the opposite conclusion, that parental lifetime income highly predicts the income of their children. For example, a child of parents in the 90th percentile has an expected income of over $100K, while a child of parents in the 10th percentile has an expected income of less than $40K.
http://www.theatlantic.com/business/archive/2015/07/america-... (which comes from http://inequality.stanford.edu/sites/default/files/economic_...)
Income isn't wealth, but I'd be surprised if the correlation isn't strong. What percentage of individuals in the US of 90th percent household wealth came from families in the top half versus bottom half growing up? I don't know off hand, but if I had to bet blindly on outcomes I'd strongly favor betting on the individual who started out better off.