Actually calling the “bra-burning feminists” unproven is kind of like saying “We don’t really know who warned people the British were coming, so how do we know it wasn’t all Paul Revere’s doing?” The origins of the bra-burning trope, and how it almost instantly became a way for anti-feminists to marginalize the feminist movement of the 60-70’s, is all pretty well documented. As is its historical context, between the idea of burning something oppressive and earlier fights for civil rights.

http://www.snopes.com/history/american/burnbra.asp

https://en.wikipedia.org/wiki/Miss_America_protest#Origin_of_.22bra-burning.22