I think that backgammon is more similar to chess than poker in this respect. Despite the exogenous element of chance it can still be considered a perfect information game.
Your statement does not hold for games truly characterised by imperfect information (e.g. poker), in theory or in practice.
It means that, in principle, it is simply a matter of running Minimax over all possible distributions on a sufficiently powerful computer, and the game can be solved. I do mean 'in principle': actually doing this is still well beyond the world's computational capabilities, though this doesn't stop computers playing stronger than any human.