It is true that, at this point, the wage gap is... at best, a bit overstated. I don't think it's an actual lie, even still. It's just that the reasons for it aren't simple, direct bias.
For example, female-dominated professions, such as education and nursing, are underpaid relative to education-equivalent male dominated professions, such as engineering and IT. Looked at on a men vs women basis for all of society, this will result in a fairly large pay gap. Looked at on a job-by-job basis, there may be no bias at all. And it's reasonable to ask how much of that pay difference is due to legitimate differences in how much society needs those jobs, and/or how many people are willing to do them, vs undervaluing of "women's work".
Another source of the pay gap is women staying home to take care of the kids. Obviously and reasonably, if a woman is out of the work force for 15 years or so, she will not be making the same as her age-mates when she returns to work. But, how much of that is reasonable reaction to the difference in experience, vs denigration or disparagement of women who didn't "put their careers first", and how much of the bias in women vs men being full-time parents is due to the actual inclinations and abilities of the parties involved vs child-care being "women's work"?
And, well, even excluding those differences in jobs and hours worked, there's still around a 5 percent difference in pay that is unaccounted-for. That is, a 5 percent overall difference in total pay even when comparing men and women who worked the *same* jobs, for the *same* hours, with the *same* qualifications. So don't try to tell me that there's no wage gap.