Well, the paper itself (referenced in the wikipedia page Wei referred to) is obviously the definitive source. The abstract reads:

This paper presents a simple, general framework for analyzing externalities in economies with incomplete markets and imperfect information. ... The approach indicates that ... equilibria in situations of imperfect information are rarely constrained Pareto optima.

All the other summaries I've ever seen also describe the result in similarly narrow terms, e.g.:

• the wikipedia entry on Joe Stiglitz, which states that

  Stiglitz has shown (together with Bruce Greenwald) that "whenever markets are incomplete and /or information is imperfect (which are true in virtually all economies), even competitive market allocation is not constrained Pareto efficient".

• the paper by Dixit that comes up as the first google hit for "Greenwald Stiglitz", which states that:

  It establishes a conceptual parallel between asymmetric information and technological externalities, andshows that a competitive equilibrium of an economy with asymmetric information is generically not even constrained Pareto efficient.

• subsequent papers by Stiglitz himself, e.g. The Invisible Hand and Welfare Economics, which describes the result in almost identical terms.

I expect that the statement Wei linked to is just a typo where someone accidentally substituted "perfect competition" for "perfect information".

ETA: I actually would have edited the wiki entry myself; but I didn't want to create the impression I'd done so just to back up my claims.