Yes, his usage is correct. I've always presumed this idiom evolved from the practice of verbally claiming something as your own. For example, a dinner guest excuses himself from the table momentarily. Before leaving, he quietly asks the hostess to please save him a piece of pie for dessert. While he's away, the other guests start helping themselves to dessert. One person reaches for the last slice of pie, and the hostess politely stops him, telling him, "I'm sorry, but that piece is already spoken for."
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