I don't see how that invalidates the original point. Taking a federally backed mortgage loan doesn't mean the government can now take your private property for public use, which is what is happening here.

If you personally buy a house using a federally backed mortgage, does that mean the government can show up and take your house and give it to someone else without compensating you? You would be OK with that if it was your house? That doesn't make sense.

This seems like a pretty blatant violation of the takings clause and is likely unconstitutional.