The possible existence of DNA evidence is apparently just an irritant for some over-zealous states and prosecutors. I read an interview (a few years ago, The New Yorker, can't remember more) with one prosecutor who, infuriated that DNA evidence overturned his case, insisted that "he knew" the accused was guilty.

However, the head scarf has deep cultural resonance and new meanings--witness all the young Muslim women who now wear them in the US.

As a diplomat, HRC is not jockeying for prestige among Western male journalists--she's showing her desire to connect with people in another cultural tradition. A western-style hat would be a block to communicating that desire and (as others above note) would convey its own messages about gendered western trad.