It turns out that the explanation is not related to 80% being the threshold before the Fed/USG would have to carry the entities on their own books. Federal Accounting Standards are silent on the issue, but the Congressional Budget Office is already treating Fannie/Freddie like USG assets/liabilities (consistent with GAAP).
Instead, the explanation is tax. Section 163 of the Internal Revenue Code generally provides that interest paid on debt is tax-deductible for federal income tax. But there's an exception. If the interest is paid on a loan from an entity that controls 80% or more of the voting power and value of a corporations' total shares, then the interest is not tax-deductible. Fannie and Freddie are generally tax-exempt. They are, however, subject to federal income tax. AIG, of course, has no tax-exempt status, whatsoever.
Because the bailout deals were structured so that the Fed or Treasury will make sizable loans to the nationalized entities, they had to be careful not to reach the 80% threshold, lest the nationalized entities (which still pay taxes) lose their tax deduction for the interest paid on the Fed/Treasury loans (LIBOR +850 on $85BN for AIG--that's a lot of interest).
Of course, one might well ask why the Treasury would want to ensure Fannie and Freddie have a deduction--that just means less revenue for the government, right? I'm not sure of the answer to this--I think there are several possible explanations, but none is overwhelming. Nonetheless, the tax explanation seems to fit better than any other.