Maybe the word "allow" was too much, but I saw in a documentary that portrayed Truman as having a big say on what happened. He talked about having seen the pictures from the Holocaust and that the Jews went through so much that it was time that they got a home. You remember that speech?
That sounds like a basic propaganda film extolling the virtues of Truman and putting him on the side of "good" in world history. The real history certainly didn't involve anyone asking his permission. Please do yourself a favor and acquire some books about the history of zionism and the history of the founding of the state of israel.
Lastly, are you sure you are not mixing up Truman with General (future president) Eisenhower, who witnessed the camps in person and this had a lasting impact on him personally? Truman did have some speeches in favor of zionism, in fact Chaim Weizmann was a close personal friend of his whom he admired, however Truman was no savior of Jews, he was an american president, he played the political games, and it was only a defiant Israeli declaration of independence which pushed the envelope and forced the parties involved to choose a side and show their cards. Truman chose against his state dept nazis, but to say that he "allowed israel to be created" flies in the face of all that we know about history. Zionism flourished from the mid to late 1800's up until 1948, and all of that set the stage for statehood. Truman had not even a political role as a US personality until he became president in 1945.
And if the US didn't react to that declaration with official recognition of a state of Israel, or if any country that reacted with recognition did not do so, the Israelis had no intention of retracting their declaration! It was not contingent on acceptance, although they wanted that.
Now read this for some additional perspective:
http://www.wymaninstitute.org/letters/2004-02-06-mom.php