John, you typed the words right out of my fingers!
WW, here's a common misconception people have about deeds. A deed is an instrument that conveys title. In the same way that you can't have your empty car come and pick you up, you can't convey somebody else's title to yourself - the person that the property was deeded to has to do the conveying.
Similarly, you don't "get people off" the deed. The new deed takes precedence over the old one. The old one is still in the records, this way we form a "chain of title," that we can search to ensure that there aren't any former owners out their with claims to the property.
But to answer your question - you heard wrong. And the scheme that David & Ken correctly identify really requires that the value of the home warrants taking over the mortgage - you don't want to take over a home that's underwater, and if it's not underwater, the owner will likely be better off selling it and pocketing a few dollars.
All the best,