Yeah, his point is a bit BS or just blatant broad brush. The Irish, esp. the Catholics, that came over as indentured servants were uneducated and piss poor. The very large numbers, again mostly Catholic, who came over from the late 1840s fleeing the famine in Ireland and through the next few decades were also pretty uneducated and piss poor. The Irish did clearly encounter prejudice and discrimination with the infamous, "No Irish Need Apply", tag line in documented records from the 1840s through to the last known in 1909.
The Protestant Irish tended to be better educated and had some means. The only "advantage" the Irish had was in being white, which allowed them to assimilate quicker. It still took a couple of generations.