[French brasier, from braise, hot coals...
bras·siere
n.
A woman's undergarment worn to support and give contour to the breasts.
Well now, there just could be a connection between these two words, now couldn't there?

I wish y'all could see the illustration Dr. Seuss drew for this one! It shows a man with what looks like half a tire around his chest, held up by shoulder straps, with hot coals therein. So, yes, Rapunzel, you're spot-on with the conflation!

And one more from the book: Medieval cathedrals were supported by flying buttocks. Dr. Seuss did NOT illustrate this one!