Earlier quoted context omitted.
The pay gap of 77c/$ still matters. Not only does the gap persist to a lower extent when you control for everything, "controlling for everything" is not actually a clarifying approach when discussing the gender gap issue. see: "The problem with controlling for 'all other factors' when looking at pay discrimination" ( https://www.reddit.com/r/badeconomics/comments/49k23i/the_pr... )
I'm sympathetic to the notion that discrimination can include subtler factors of pushing women into lower pay positions. However, the problem with the 77 cent figure is that it's frequently stated like this: "women get paid only 77% of what men do for the same jobs." Which is entirely false. Yet, if you asked most people about the 77 cents figure they'd think it actually meant women got paid much less to do the same…
The "same job" is a subjective distinction, so you can't say it's entirely false; it's really a matter of opinion.