An interesting study, the data of which, I have not verified.
If the poverty rates for each educational bin remained the same, then the upward redistribution of adults from the lower bins to the higher bins would have led to lower overall poverty. But that's not what happened.
The big things that cause poverty for adults over the age of 25 in a low-welfare capitalist society—old-age, disability, unemployment, having children—do not go away just because you have a better degree.
I'll also throw in that an education can also generate significant debt by the time you are 25.