In a way I think Jezebel's explanation that adding text to an AutoShape
converts it to a text box makes about as much sense as any other. I had been
thinking of it as being a text box merged with the AutoShape (as opposed to
a text box added in front of an AutoShape).
The important thing to know, no matter how you view it, is that the text
area is always rectangular regardless of the shape of the object. You can
increase the available area somewhat by setting the text box margins to 0,
but if you want text to completely fill the shape, the only way to achieve
this is to place a text box (with No Line and No Fill) in front of the
shape, centering the text, and then using line breaks to make the shape of
the text match the underlying shape.