'Tis I (Ken Perko). Forget all that stuff about non-alternating amphicheirals (which belongs elsewhere) and just flip the second conjecture around to read something like "An amphicheiral (or acheiral) alternating link has zero writhe." Prior editing got this one backwards. I'm sure you can find sources in Lickorish's text for this well known result which goes back to Kauffman-Thistlethwaite-Murasugi's work with the Jones polynomial.