As a GSE, it is a privately-owned corporation authorized to make loans and loan guarantees. It is not backed or funded by the US Government, nor do the securities it issues benefit from any government guarantee or protection.
Freddy Mac losses are not insured for by the US Government, so I don’t see how this is a taxpayer bailout. If they assume risky Alt-A mortgages then they are digging their own grave just like the other lenders that have perished.