It is wrong, no offense. Mortgage backed debt is just a debt instrument payments from which depend on mortgage payments. It isn't debt issued by a business that has a bunch of mortgage loans on its books- those sorts of things don't exist anymore.
The mortgage industry is bewilderingly complex but short version is- most loans are almost immediately sold to Fannie or Freddie, not kept on the books of those who made them. Fannie and Freddie then securitize- make bonds out of combinations of those loans- a large portion, tho not all of loans they buy. The Fed is buying a lot of those bonds, probably generally the ones backed by the most risky payers, but the analysis is extremely nuanced.
That is why the Fed owns 1/3 of bonds, which (only) equate to 11% of total loan value. This prop on the market is much more powerful than 11% suggests.