However, being a pass-through has nothing to do with whether they own the assets.
No, the assets, the mortgages, are put in the trust.
From the link I sent you earlier:
Freddie Mac may from time to time (i) retain, reacquire or purchase mortgage-related securities and other mortgage-related assets that are referred to herein as “Assets” in accordance with the applicable provisions of the Freddie Mac Act, (ii) as Depositor, transfer and deposit such Assets into various trust funds