Maybe, but Reddit doesn't strike me as the sort of place with pay bands in that sense. I suppose they could fabricate a new title, and suggest it makes more money, but you can only go so far with that.
Of course, I can see managers trying that, but I presume that her directive would mean that any alteration of the offer, other than the equity alterations suggested, would be rejected at HR. As a manager, you have to have your opening approved, including title, before you can even interview people. HR also drafts the offer letter and approves the terms. Negotiations can cause the title or the pay to change, but I'm guessing that unless she's not sincere about this, she's not permitting title changes with different compensation after the offer.
Here's the thing. I probably make more than some people due to negotiations, but I probably make less than others based on the same. Honestly, unless I am truly getting screwed, as long as my needs are met, I don't care if someone makes more than I do. There are also some people out there who have families or child support payments or a sick mother or something who would benefit from the extra money and lobbied to get it.
A woman needs to do only do one thing. After researching the salary she feels is fair for the position, she decides if she is comfortable with it or not. If she is, then stick to that number come hell or high water. She's not in a competition to figure out who makes more than her, she should be just trying to live her life successfully. If she wants a Mercedes to drive around in and she needs X amount to get it, then she needs to ask for X.
While I understand that it seems unfair that women may make less because they don't negotiate, negotiation is nothing more than knowing your real number and being willing to walk away if they can't give it to you. You can point blank tell someone your actual number and tell them that if they can make it, you will start. If they can't, then this is her first, best, and final offer. If an adult woman can't figure that number out for herself and stick to it, then no "no negotiation" policy is ever going to help her.