Interesting question. I would call it a purchase as while the borrower previously owned 1/3 of the home, this loan would be to purchase the other 2/3 and to me, that's still "purchasing" a home. I guess i'd equate it somewhat to a regular 80% purchase loan in a way....the loan by itself didn't buy the home, but combined with the down payment it did; similarly this loan doesn't by itself buy the home, but with the 1/3 interest the borrower already had, it does.
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I'm fixin' to fix that.