Verse 12 doesn't say the slave said he hadn't - it says he hadn't: "And when he had eaten them his spirit returned, and he was refreshed: for he had not eaten bread, nor drunk water three days, and three nights."
Perhaps his master began withholding food from the slave when he saw the man was getting sick. He saw no reason to squander resources.
Iow, if the text says the slave hadn’t eaten for three days and three nights, why should we assume that’s not true? It very likely is true, since that’s the way it’s expressed.