That doesn't mean as much as it sounds like it does, though. Suppose an organization has $100 of "houses only" money, and another $100 of "general fund" money,

That doesn't mean as much as it sounds like it does, though. Suppose an organization has $100 of "houses only" money, and another $100 of "general fund" money, $20 of which is also spent on houses. Now say I donate $5 of my own money to "houses only". There is absolutely nothing stopping the org from (and arguably nothing wrong with) reducing the "general fund" spending on houses by $5, so that the ultimate amount that goes to houses is unchanged.