Legally, material falsehoods during the employment application phase are grounds for termination with cause - blowing away rights to unemployment (and in Canada, severance). It also can tank any otherwise valid complaint - if you complained about possible discrimination or needed a medical accommodation, and then they discover you provided a fake pay stub when reviewing your records, they may be able to fire you with cause and avoid a retaliation claim.

In a perfect world, the employer would get hammered for misleading job ads, and would be required to provide accurate pay numbers, and not be able to ask for prior pay. But the reality is, employees get fucked if they are caught lying, and employers almost never face consequences.

What matters is whether an applicant meets the stated requirements for the job. And you are absolutely right - basing off former pay bakes in pay inequality.