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When the Ven Thanissaro Bhikkhu says "solid center" he's not talking about literally having something inside your body that is physically solid, and he's definitely not saying about some sort of true self (His other writings make it clear that he accepts the orthodox position that there is no ultimately real true self). What he means is that the goal of meditation is to find happiness which isn't dependent on causes and conditions, and therefore cannot be disturbed, so metaphorically you can say that it is solid or unbreakable.
I've never heard of this particular parable, but it sounds to me like it is a parable about the pointlessness of developing any kind of view of self.