The IDB editorial strikes me as talking points, YMMV.
The Post and AEI had stronger reporting. There is no doubt that the GSE's accounting practices were scandalous. Their lobbying was over the top. The contention that they bought subprime MBS in a misguided attempt to curry favor from Congress in the aftermath of the accounting scandal is interesting - not sure it is the whole story but it is plausible enough to be a good chunk of the story. In matters of business, I think good old greed is always a part of equation. Therefore, there is always the possibility that the GSE's thought these MBS might turn out to be good investments.
It is important to keep in mind that during this time, the SE's were doing other things that further the affordable housing mission - most notably they were large buyers of Low Income Housing Tax Credits. IMHO, a much better way of encouraging affordable housing than buying subprime MBS (at least as long as you have tax liability

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Maybe we have different standards for what constitutes encouragement of bad underwriting. The Post article suggests that had Fannie and Freddie actually bought whole loans it would have enforced better underwriting. "But because Fannie and Freddie were buying mortgage-backed securities rather than the actual subprime loans, their involvement came too late to require stiffer standards from lenders." They bought the highest-rated pieces; that doesn't rise to the level of encouragement to me. The folks who bought the less-than-AAA slices were providing way more encouragement. Again, YMMV.
Contrary to what AEI suggests - the sides were not that far apart - a deal could have been made between President Bush and Congress that would have reined in the GSE's in 2005. That was a huge missed opportunity that everyone involved, if they were honest about it, would admit to.