If Rudy Giuliani becomes President, could it not be argued that Al-Qaeda put him into power?

Rudy Giuliani gained national recognition after 9/11. He was named Person of the Year by the New York Times, he was knighted by Queen Elizabeth, and now he's a leading candidate for the Presidency. If it wasn't for the Al-Qaeda attacks on 9/11, none of that would've happened. So apparently 9/11 was great for his political career. If he wins the presidental election, it seems like he would owe his success to Al-Qaeda. Everyone says we won't let ourselves be influenced by terrorists, but if Giuliani becomes president then aren't we letting them influence one of the biggest decisions we ever make? What do you think?