> I'm hesitant to call BS

I'm not - it is bullshit.

If she earned the top of the band, she was by definition not underpaid. She in fact earned more than every other employee that was not top of the band.

She might have wanted more money for what she was doing (and it has my sympathy, I too like more money).

But the solution was to either be promoted - which she may not have wanted, and I am sympathetic to that, I also don't enjoy promotions - or to move to a company that paid more for that role.