The protocol you describe satisfies 2 and 3 but not 1, so when that protocol is adopted, 1 is wrong.
The correct form of statement 1 is that 75% is a maximum win rate if each player must choose a strategy that is contingent on the realization of some classical random variable (so that in particular there exists a joint distribution for the set of all random variables that are available for at least one player to use).
In a world governed by classical physics, this correct form of statement 1 is equivalent to the statement you've given about information exchange. In that world, all observables can be modeled as classical random variables.
But for some sets of quantum observables, that's no longer true, so in a world governed by quantum mechanics the two forms of Statement 1 are not equivalent. In your example, if we take four observables --- the outcome of Player $i$'s measurement with the device in position $j$, where $i$ and $j$ each have two possible values --- there is no joint probability distribution for the outcomes (i.e. they cannot be modeled as classical random variables satisfying Kolmogorov's axioms).