You'll have to take the matter up with respected WWII histortian James Bradley, author of this account, Flags of our Fathers, and Imperial Cruise. To be honest, I'm not sure what you're disputing here, but past experience tells me that you tend to feel entitled to your own facts to go with your curious opinions.
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A correction is not a dispute. And facts are neither yours nor mine.
You may rely on a novelist for what you think are the facts...some of us prefer to do our own work and have read the USN's own account which is available on line.
http://www.history.navy.mil/faqs/faq10-1.htm
The US navy began strikes against the island of Iwo Jima on June 15th, 1944. The first American casualty was suffered two days later when a member of an underwater demolition team was struck and killed by small arms resistance. The campaign against Chichi was undertaken only because the Japanese were using it to reinforce Iwo Jima. The island itself had no stategic value, and the Americans never bothered to take it until the war was over.
And Bradley never wrote a novle that I am aware of.