Also from the article
>Research by economists from Harvard and Berkeley found that fewer than 10 percent of people in the bottom fifth of the wealth distribution will make it into the top fifth.
Poverty is an arbitrary threshold. Its definition if you Google it is "the state of being extremely poor" and as you noted, you can eliminate poverty by reducing the threshold. This is why the article chose quintiles.
As someone else said here, the article is bringing attention to a problem--lack of intergenerational social mobility. This has a lot of implications, one of which is that families born into poverty are unlikely to get out. It has other implications too, such as that middle class families will stay middle class and the elite stay elite. From what I have seen, the middle class are pretty happy being middle class and the elite like being elite, but the anxiety and stress of the low-income lifestyle is pretty horrible for people living in it.
If people were happy at all tiers of the socioeconomic ladder, social mobility wouldn't be worth discussing. We brought up poverty because those are the people who are suffering the worst.
As for living better than Aztec kings, that's too sweeping a claim. Aztec kings might not have been able to enjoy hot pockets or McDonalds, but they knew they were going to have dinner every night.
Edit: I know what you're both saying that being in the bottom 20% does not imply a low standard of living in the same way that being in poverty does. But in the US, the bottom 20% implies a low standard of living. The median net worth for the bottom 20% in 2011 was about -$6,000 [1], which means the lowest income households are consuming more wealth than they are creating. Combine this with the article's thesis that people are stuck in their quintile, and it's a statement that our nation's poorest are not able to escape a cycle of living off subsidies, presumably from the government.
http://www.census.gov/people/wealth/files/Wealth%20distribut...