The human genome has 6 billion bases, not 6 billion bits. Each base can take one of 4 values, so significantly more data than binary. But maybe not enough of a difference to affect your point.
So six billion bits since two bits can represent four values. Base pairs and bases are effectively the same because (from the link) "the identity of one of the bases in the pair determines the other member of the pair."
It's 6 billion because you have 2 copies of each chromosome. So 12 billion bits right? But I do think your original point stands. I'm mostly being pedantic.
