Here is a more complete passage of Bradley's testimony:
I am under no illusion that our present strategy of using means short of total war to achieve our ends and oppose communism is a guarantee that a world war will not be thrust upon us. But a policy of patience and determination without provoking a world war, while we improve our military power, is one which we believe we must continue to follow….
Under present circumstances, we have recommended against enlarging the war from Korea to also include Red China. The course of action often described as a limited war with Red China would increase the risk we are taking by engaging too much of our power in an area that is not the critical strategic prize.
Red China is not the powerful nation seeking to dominate the world. Frankly, in the opinion of the Joint Chiefs of Staff, this strategy would involve us in the wrong war, at the wrong place, at the wrong time, and with the wrong enemy.
— From testimony before the Senate Committees on Armed Services and Foreign Relations, May 15, 1951.—Military Situation in the Far East, hearings, 82d Congress, 1st session, part 2, p. 732 (1951).