A few but influential papers in macroeconomics cite a working paper titled "The Kuhn-Tucker Theorem Implies the Transversality Condition at Infinity" by P. Romer (yes, that Paul Romer) and T. Shinotsuka that apparently only circulated intramurally at the University of Rochester. While this means its content can only be inferred, the context in which it is cited suggests that for an infinite horizon optimal control problem $$ \max_u \sum_{t=0}^\infty f(x_{t},u_{t},t) \quad \text{s.t.} \quad x_{t+1} \leq g(u_{t},x_{t}) $$ a transversality condition (along, of course, with the usual first-order conditions) of the form $$ \lim_{t \to \infty} p_{t}x_{t+1} =0 $$ where $p_{t}$ is the co-state variable, is "necessary and sufficient for an optimum." Further, of course, the paper's title claims that this results follows from the Karush-Kuhn-Tucker theorem.
Now the fact that it was never published could only mean one of two things: the result was trivial (and/or already proven), or it was incorrect. Does anybody have an idea what the line of argument could have been, and where it is wrong? Or, in case of the former, does anyone know if and where a result like this has been proven?