That's a pretty interesting paper but I'm not convinced that the evidence presented backs up its conclusions. One of the things they do is measure various parameters relative to 7 different affordable housing goal criteria (such as loans to census tracts with median income of 80% or less than the median income of the metropolitan area). However, the authors don't seem to address the problem of separating the effects of each different criteria. Also, the data is fairly limited (only from 3 years, in 2 states) and they make some pretty strident assumptions. For example, they can't seem to find a possible causal link between the state of the real estate market in the mid 2000s and an increase in mortgages spurred by affordable housing legislation several years prior to their 2004-2006 window.
To me though it seems obvious that putting more people into the housing market, especially while it is experiencing a moderate boom would simply amplify that boom, as folks who managed to end up with some positive equity would work to maintain it, "flip" their properties, etc. As long as the market was always going up and people could generate positive equity just by sitting on their ass defaults were rare, because it would have been easy for people to sell their properties if they couldn't make payments in the future. Also, a lot of these mortgages were designed for flipping, having low payments early on before balloon payments later, making it easier to avoid default in the early years. On the other side of the equation, investors ate up securitized mortgages while the market was going up because they thought there was no risk. If people defaulted on their mortgages the properties would just be foreclosed on and since the property would inevitably have a higher market value than the mortgage, there was no downside for the investors. Which works just fine until the market reaches its breaking point and stalls out, after which people start going underwater on their mortgages, defaults increase, valuations fall, and everything goes to hell, as we saw.
The paper addresses the proposition of affordable housing legislation causing an excess in sub-prime lending just prior to the peak of the real estate boom. However, it fails to address the more important and more basic question of whether affordable housing legislation injected an excess of "unqualified" buyers into the housing market, distorting the market and leading to a bigger boom and a bigger bust.
However, as I mentioned, that whole mess (regardless of its cause) has only contributed a comparatively small amount to the much larger sovereign debt crisis that the world is facing now, which would take a lot of stretching to blame on the market.