When I make it precise, it is a tautology. Define a "strictly competitive game" as one in which all 'pure outcomes' (i.e. results of pure strategies by all players) are Pareto optimal. Then, in any game which is not 'strictly competitive', cooperation can result in an outcome that is Pareto optimal - i.e. better for both players than any outcome that can be achieved without cooperation.

The "counter-example" you supplied is 'strictly competitive'. Some game theory authors take 'strictly competitive' to be synonymous with 'zero sum'. Some, I now learn, do not.