No it doesn’t. The company is fundamentally in a much better negotiating position (they have much more data on salaries) and carry way less risk than the employee (a company has many employees, each employee has just one job).
In each negotiation about a position, the company is negotiating only about one of its many positions; the candidate[1] about what will (usually) be their only job. And companies usually, AFAIK, get a lot more applications[1] per position than each applicant[1] gets offers per job search.
So no, AFAICS you are wrong and the original thesis of "the company holds the advantage" is correct.
