Well, what you said is this.
> FM does not guarantee most mortgages, only certain govt types like FHA and VA loans, which the govt decided to back in order to help low income people get loans (otherwise the rates would be even higher for them).
And this.
> The OP claimed they guaranteed mortgages, which they do not.
So it read to me like they don't guarantee mortgages save for the "special" mortgages for underserved groups (FHA/VA). In fact, they do. They guarantee all the loans they buy, as far as I know. They only buy conforming loans. Conforming loans are another way of saying, loans that they will buy (and guarantee). Of course they don't guarantee loans they don't buy.
I used to work at a mortgage originator, and we sold the majority of our loans to Fannie and Freddie.
> Of all conforming loans made, Freddie and Fannie end up purchasing about 60% of those.
This is true, because private investors pay more than Freddie and Fannie for conforming loans.