They can hire anyone, I can work anywhere. In a properly functioning market, neither side should have any problem walking away from the table if the other side is being unreasonable.
In practice though, companies can survive for months or even years without filling a position and the hiring manager rarely suffers directly for any inefficiency created by not filling a position, while most people can go only for a short period of time without a job before their quality of life starts to suffer. At the same time, corporate consolidation means that in many areas (both geographic and technical) there are only a few major employers, meaning that being blacklisted by any one could be catastrophic for someone's career and meaning only a small number of individuals need to act in unison to manipulate the labor market (driving wages down, spreading bad hr practices, etc), basically all the problems of any other oligopoly. There is an asymmetry of information: the individual will only take on a few jobs over the course of their career and can not afford to experiment much as they go - for any given point in their lifetime, they're basically working with a sample size of 1; even a moderately sized employer on the other hand might hire dozens and interview thousands of people a year and have records of such recruiting data going back decades. Finally there is a social asymmetry - a company trying to poach an employee will likely not face any negative consequences for it, but an employee simply looking at what options are out there could potentially be viewed as disloyal and either be fired or removed from advancement tracks intended for long-term employees - a simple phone call to check a person's references could potentially put them into a much worse negotiating position. None of these issues are inherent, they pretty much all stem from weak labor laws and inadequate social safety nets.