Not to defend dishonest interpretations of science here, but... "heritability" sounds like a unfortunate choice of word for the concept described. It invites inadvertent misrepresentations.

I'm reminded of an old OB comment by Anatoly Vorobey that made the reasonable point that Kolmogorov complexity captures the human notion of "complexity" very lousily at best. (WTF, the whole universe is less complex than one planet within it?) So too it seems with "heritability". People clearly want a number that would describe "how much the over-all level of the trait is under genetic control, and... how much the trait can change under environmental interventions" - why can't the biologists just give them that?