What kind of correct inference could possibly be drawn? The data is arbitrarily scaled to begin with. By criticizing the interpretation of the log graph, it seems to me you've implicitly accepted that the authors' quantification of happiness is a meaningful measure, that it makes sense to say that one level of happiness is twice as much as another and that asking someone to imagine a ladder can establish that.
Tucked away in a footnote in the paper: "We should add a caveat, that this inference of 'diminishing marginal well-being' requires taking a stronger stand on the appropriate cardinalization of subjective well-being (Oswald 2008)." You say caveat, I say giant ontological turd hitting the fan...